Here is a list, in alphabetic order, of the scripts developed for the Math 160 class. Each script name is a link to a table entry that gives more information about the script.
• assess_normality(): generates quantile points and a plot to help assess if a set of values is normally distributed
• ci_2known(): generates a confidence interval for the difference of means for two populations assuming we know the standard deviation of the underlying populations
• ci_2popproportion(): generates a confidence interval for the difference of the proportion of some characteristic in two populations
• ci_2popvar(): generates a confidence interval for the ratio of the variances in two populations
• ci_2unknown(): generates a confidence interval for the difference of means for two populations assuming we do not know the standard deviation of the underlying populations
• ci_known(): generates a confidence interval for the mean of a populations assuming we know the standard deviation of the underlying population
• ci_prop(): generates a confidence interval for the proportion of some characteristic in a population
• ci_stddev(): generates a confidence interval for the standard deviation in a population
• ci_unknown(): generates a confidence interval for the mean of a population assuming we do not know the standard deviation of the underlying population
• collate3(): creates groupings (bins, buckets) for a list of values and determines values for the frequencies in those groupings
• crosstab(): generates a χ² analysis and cross tabuation tables for a matrix of values
• dot_plot(): generates a dot plot of the values in a list
• find_percentile(): This function, based on a given list of values and a goal value, computes the percentile for that goal value in the given list.
• find_samp_size(): computes the minimal sample to get a desired margin of error when the population standard deviation is known
• get_from_table(): This script takes the low and high values for the first interval of a interval-based frequency table, along with a list of the frequencies for the intervals and produces the sum of the frequencies, the approximate mean of the data, and the standard deviation of the data based on using the midpoint values of each interval the given frequency number of times. The script also produces a new variable `from_table_x` that holds all of those midpoint values.
• gnrnd4(): Used to generate sets of values according to specified key values. This allows the generation of values that match those given on web pages that use the corresponding Javascript function.
• gnrnd5(): Used to generate sets of values according to specified key values. This allows the generation of values that match those given on web pages that use the corresponding Javascript function.
• goodfit(): Runs the χ² test for the goodness of fit.
• hypoth_2test_known() : tests the hypothesis of equal means for two populations assuming we know the standard deviations of those populations
• hypoth_2test_prop() : tests the hypothesis of equal proportions for two populations
• hypoth_2test_unknown(): tests the hypothesis of equal means for two populations assuming we do not know the standard deviations of those populations
• hypoth_2test_var(): tests the hypothesis of equal variances for two populations
• hypoth_test_known() : tests the hypothesis for the mean of a population assuming we know the standard deviation of that population
• hypoth_test_prop() : tests the hypothesis for the proportion of a characteristic in a population
• hypoth_test_sigma(): tests the hypothesis for the standard deviation of a population
• hypoth_test_unknown(): tests the hypothesis for the mean of a population assuming we do not know the standard deviation of that population
• long_summary(): duplicates and augments the built-in summary() function
• make_freq_table(): creates a frequency table for a list of discrete values
• Mode(): finds the mode of a list of values (note the need for the upper-case M)
• model(): does nothing...it is just a convenient starting point for a new script
• nCr(): gives the number of combinations of n things taken r at a time
• nPr(): gives the number of permutations of n things taken r at a time
• num_comb(): gives the number of cobbinations of n things taken r at a time
• num_perm(): gives the number of permutations of n things taken r at a time
• papfleton(): gives probability for the Apfelton distribution
• pbinomeq(): finds the binomial distribution probability of getting exactly a number of successes in a given number of trials
• pblumenkopf(): gives probability for the Blumenkopf distribution
• qapfleton(): gives x value for given probability in the Apfelton distribution
• qblumenkopf(): gives x value for given probability in the Blumenkopf distribution
• pop_sd(): finds the standard deviation of a list of values, assuming those values are the population rather than a sample
• pprop(): Computes the normal approximation for the probability of getting phat (or less) from a proportion with probability of success p and sample size n.
• shuffle(): creates a shuffled version of a list of values
• stem_leaf(): creates a stem and leaf listing of values
The following table summarizes the scripts that I have developed for the class. The items are in alphabetic order by file name, which may be different from the function name. The table gives the script name, the a link to a file that holds the script, and a brief description of the script. For almost all of the descriptions there is an example giving R statements that demonstrate the use of the function. For the most part there is one function per file. However, there are instances where there is more than one script in a file.

 Important note: The `source( )` statements included in the detailed descriptions below assume that the sample script is being run from a directory (folder) that is a sub-directory (sub-folder) that is a "child" of the directory (folder) holding the scripts being explained.

 Script Name File Names Brief Description of what the script does papfelton() qapfelton() apfelton.R Probability density functions for the Apfelton Distribution (see web pages) Examples: ```source("../apfelton.R") # load the function papfelton(2.34) # returns area to the left of 2.34 papfelton( 1.74, lower.tail=FALSE) # returns area to # the right of 1.74 qapfelton( 0.783 ) # returns x value that has # 0.783 area to its left qapfelton( 0.145, lower.tail=FALSE ) # returns x value # that has 0.145 area to its right ``` assess_normality() assess_normality.R Produces a plot to help assess if a set of values is normally distributed. Example: ```source("../gnrnd4.R") # be sure gnrnd4() is loaded gnrnd4(1394565804,8300542) # generate some values source("../assess_normality.R") # be sure # ssess_normality() is loaded assess_normality( L1 ) # do the work, create the plot ``` pblumenkopf() qblumenkopf() blumenkopf.R Probability density functions for the Blumenkopf Distribution (see web pages) Examples: ```source("../blumenkopf.R") # load the function pblumenkopf(2.34) # returns area to the left of 2.34 pblumenkopf( 1.74, lower.tail=FALSE) # returns area to # the right of 1.74 qblumenkopf( 0.783 ) # returns x value that has # 0.783 area to its left qblumenkopf( 0.145, lower.tail=FALSE ) # returns x value # that has 0.145 area to its right ``` ci_2known() ci_2known.R Finds the confidence interval for a the difference of two population means where we know both population standard deviation, sigma_1 and sigma_2, and we have a samples of size n_1 and n_2 with sample means xbar_1 and xbar_2. Example: ```# set up the problem # know the population standard deviations sigma_1 <- 11.3 # for 1st population sigma_2 <- 13.8 # for 2nd population # set values for the two samples n_1 <- 57 # size of 1st sample xbar_1 <- 34.76 # mean of 1st sample n_2 <- 41 # size of 2nd sample xbar_2 <- 37.41 # mean of 2nd sample source("../ci_2known.R") # load function # get a 97.5% confidence interval for mean_1 - mean_2 ci_2known( sigma_1, n_1, xbar_1, sigma_2, n_2, xbar_2, 0.975) ``` ci_2popproportion() ci_2popproport.R Finds the confidence interval for a the difference of two population proportions where we have a samples of size n_1 and n_2 with sample successes called x_1 and x_2. Example: ```# set up problem n_1 <- 76 # size of first sample # number of items with characteristic in x_1 <- 37 # first sample n_2 <- 93 # size of second sample # number of items with characteristic in x_2 <- 44 # second sample c_level <- 0.95 # set confience level to 0.95 # be sure function is in environment source("../ci_2popproport.R") # run the function ci_2popproportion( n_1, x_1, n_2, x_2, c_level ) ``` ci_2popvar() ci_2popvar.R Finds the confidence interval for the ratio of two population variances where we have a samples of size n_1 and n_2 with sample standard deviations called s_1 and s_2. Example: ```# set up problem n_1 <- 34 # number of items in numerator sample s_1 <- 12.4 # standard deviation of numerator sample n_2 <- 52 # number of items in denominator sample s_2 <- 11.3 # standard deviation of denominator sample c_level <- 0.90 # set the confidence level # be sure function is in environment source("../ci_2popvar.R") # run the function ci_2popvar( n_1, s_1, n_2, s_2, c_level) ``` ci_2unknown() ci_2unknown.R Finds the confidence interval for a the difference of two population means where we do not know the population standard deviation and we have a samples of size n_1 and n_2 with sample means xbar_1 and xbar_2, and sample standard deviations s_1 and s_2. Results are given for both the simple degrees of freedom and the computed degrees of freedom. ```# set up the problem # do not know the population standard deviations # set values for the two samples n_1 <- 57 # size of 1st sample xbar_1 <- 34.76 # mean of 1st sample s_1 <- 11.3 # standard deviation of 1st sample n_2 <- 41 # size of 2nd sample xbar_2 <- 37.41 # mean of 2nd samples s_2 <- 13.8 # standard deviation of 2nd sample source("../ci_2unknown.R") # load function # get a 97.5% confidence interval for mean_1 - mean_2 ci_2unknown( s_1, n_1, xbar_1, s_2, n_2, xbar_2, 0.975) ``` ci_known() ci_known.R Finds the confidence interval for a popultion mean where we know the population standard deviation sigma and we have a sample of size n_1 with a sample mean xbar_1. Example: ```# set up problem sigma <- 4.56 # known standard dev. of population n_1 <- 34 # sample size xbar_1 <- 28.4 # sample mean c_level <-0.85 # confidence level set to 0.85 # be sure that the function is loaded source("../ci_known.R") # run the fnction ci_known( sigma, n_1, xbar_1, c_level ) ``` ci_prop() ci_prop.R Computes a confidence interval for the proportion given the sample size, the number of items with the characteristic, and the confidence level. Example: ```# set up problem n_1 <- 65 # size of sample # number of items in sample with x_1 <- 24 # the desired characteristic c_level <- 0.95 # set confidence level to be 0.95 # be sure function is loaded source("../ci_prop.R") # run the function ci_prop( n_1, x_1, c_level ) ``` ci_stddev() ci_stddev.R Finds the confidence interval for a population standard deviation based on a sample size, sample standard deviation, and confidence level desired. Example: ```# set up problem n_1 <- 26 # size of the sample s_1 <- 5.34 # set standard dev. of sample c_level <- 0.925 # set confidence level to 0.925 # make sure function is loaded source("../ci_stddev.R") # run function ci_stddev( n_1, s_1, c_level ) ``` ci_unknown() ci_unknown.R Finds the confidence interval for a population mean where we do not know the population standard deviation but we do have a sample of size n_1 with a sample mean xbar_1 and a sample standard deviation s_1. Example: ```# set up problem s_1 <- 4.56 # standard dev. of sample n_1 <- 34 # sample size xbar_1 <- 28.4 # sample mean c_level <-0.85 # confidence level set to 0.85 # be sure that the function is loaded source("../ci_unknown.R") # run the fnction ci_unknown( s_1, n_1, xbar_1, c_level ) ``` collate3() collate3.R This script produces a frequency table for non-discrete data. The script is often run twice, first with just the data specified and second, based upon the output of the first run, with the data, the low value of the first "bucket" and the bucket width. The name is left over from a program developed on the TI83/84 calculators to do the same thing. Example: ```# set up problem # first generate some values source("../gnrnd4.R") gnrnd4(2768424504,142513276) # look at the data L1 # be sure the function is loaded source("../collate3.R") # run it the first time collate3( L1 ) # the output of that will give us # a good idea of the low value for the # first "bucket", and the width of # the buckets. Here we will use 105 # and 5 respectively low_val <- 105 bucket_width <- 5 collate3( L1, use_low=low_val, use_width=bucket_width) # # by default these are closed on the # right, we will run again, closed on # the left and we will store and then # view the result holder <- collate3( L1, use_low=low_val, use_width=bucket_width, right=FALSE) View( holder ) # note the capital V ``` num_comb() nCr() num_perm() nPr() combinations.R Functions to do combinations of n things taken r at a time. (Note this includes the functions for permutations as well.) Example: ```# make sure the functions are loaded source("../combinations.R") # that actually loads four functions # num_comb(), nCr(), num_perm(), and # nPr() # run each for 8 things taken 3 at a time num_comb( 8, 3 ) nCr( 8, 3 ) num_perm( 8, 3 ) nPr( 8, 3 ) ``` crosstab() crosstab.R Function to provide not only the cross tabulation for a matrix but also to provide the expected values, the row, column, and total percents, and the intermediate steps to perform a χ² test for independence on the original matrix. Example: ```# set up the problem # first we will generate a crosstab matrix source("../gnrnd4.R") gnrnd4( key1=783566808, key2=8756454753 ) # then look at it matrix_A # now be sure the function is loaded source("../crosstab.R") # run the function crosstab( matrix_A ) # this produces a little consol output and # numerous tabs in the editor pane ``` dot_plot() dot_plot.R Produces a dot plot of the data. Example: ```# set up the problem # first we will generate a list of values source("../gnrnd4.R") gnrnd4( 507093402, 1200148 ) # then look at it L1 # now be sure the function is loaded source("../dot_plot.R") # run the function dot_plot( L1 ) # this produces a dot plot of the values ``` find_percentile() find_percentile.R This function, based on a given list of values and a goal value, computes the percentile for that goal value in the given list. Example: ```# set up the problem # Assuming L1 holds a list of numeric values goal_val <- 348 # we want to know the percentile for # 348 in that listed # now be sure the function is loaded source("../find_percentile.R") # run the function find_percentile( L1, goal_val ) ``` find_samp_size() findsampsize.R For confidence intervals for the population mean, this function finds the required sample size for a desired margin of error value given the population standard deviation and the confidence level. Example: ```# set up the problem sigma <- 13.24 # the population std. dev. c_level <- 0.95 # set confidence level at 0.95 m_o_e <- 2.75 # the desired margin of error # now be sure the function is loaded source("../findsampsize.R") # run the function find_samp_size( sigma, c_level, m_o_e ) ``` get_from_table() get_from_table.R This script takes the low and high values for the first interval of a interval-based frequency table, along with a list of the frequencies for the intervals and produces the sum of the frequencies, the approximate mean of the data, and the standard deviation of the data based on using the midpoint values of each interval the given frequency number of times. The script also produces a new variable `from_table_x` that holds all of those midpoint values. Example: ```# be sure the function is loaded source("../get_from_table.R") # run the program. We need to give the # program the low and high values of # the first interval of the frequency tabe, # followed by the list of interval frequencies. # The command below assumes that the first # interval is from 19 to 36 and that there are # six intervals with the frequencies 23, 28, 15, # 32, 19, and 27 get_from_table( 19, 36, c(23, 28, 15, 32, 19, 27) ) # along with the output of the funtion we get # a new variable that holds the midpoints repeated # the number of times given by the frequencies from_table_x # then look at the list of midpoints ``` gnrnd4() gnrnd4.R This script generates data in the variable L1, and possibly in L2, depending upon two, or three, keys that are supplied as arguments to the function. It is typical to have these arguments supplied on test questions so that you can create tables of data that are identical to those given on the test. The use of the function is described in gnrnd4.htm. Example: ```# be sure the function is loaded source("../gnrnd4.R") # run the program, the various key # values are usually given on some # web page, but we could read the # documentation to understand them gnrnd4( 1607653804, 11300762) L1 # then look at the result ``` gnrnd5() gnrnd5.R This script generates data in the variable L1, and possibly in L2, or in one case, in matrix_A depending upon two, or three, keys that are supplied as arguments to the function. It is typical to have these arguments supplied on test questions so that you can create tables of data that are identical to those given on the test. The use of the function is described in gnrnd5.htm. Example: ```# be sure the function is loaded source("../gnrnd5.R") # run the program, the various key # values are usually given on some # web page, but we could read the # documentation to understand them gnrnd5( 160765003804, 113000762) L1 # then look at the result ``` goodfit() goodfit.R For problems where we mave multiple categories and we have a null hypothesis stating the probability (proportion) for each category, and we have the frequency of each category in some sample, this will do a χ² test on the goodness of fit for that sample against the null hypothesis. Example: ```# set up the problem sig_level <- 0.05 # the significance level of the test cat_names <- 1:5 # the names of the categories, here 1, 2, 3, 4, 5 H_0 <- c(3, 5, 3, 7, 2)/20 # theproportions in the null hypothesis obs <- c(11, 38, 25, 36, 10) # the observed frequencies auto_view <- TRUE # forces the function to display a fancy table # now be sure the function is loaded source("../goodfit.R") # run the function goodfit( cat_names, H_0, obs, sig_level, auto_view ) ``` hypoth_2test_known() hypo_2known.R This script performs a test on H0: &mu1; - μ2 = 0 against one of the standard alterntive hypotheses based on two samples, of size n_1 and n_2, that give us a sample means xbar_1 and xbar_2, and where we know the standard deviations, sigma_1 and sigma_2 of the underlying populations. We also need to specify the desired level of significance. Example: ```# set up problem sigma_1 <- 4.32 # population 1 std. dev. sigma_2 <- 5.71 # population 2 std. dev. n_1 <- 45 # sample 1 size xbar_1 <- 56.2 # sample 1 mean n_2 <- 58 # sample 2 size xbar_2 <- 57.9 # sample 2 mean # set up the type of test H_type <- -1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_2known.R") # run function hypoth_2test_known( sigma_1, n_1, xbar_1, sigma_2, n_2, xbar_2, H_type, alpha ) ``` hypoth_2test_prop() hypo_2popproport.R This script performs a test on H0: p1; - p2 = 0 against one of the standard alterntive hypotheses based on two samples, of size n_1 and n_2, that give us a sample success counts x_1 and x_2. We also need to specify the desired level of significance. Example: ```# set up problem # number of items in sample 1 x_1 <- 39 # with characteristic n_1 <- 83 # size of sample 1 # number of items in sample 2 x_2 <- 44 # with characteristic n_2 <- 125 # size of sample 2 H_type <- 0 # neg for <, 0 for !=, pos for > alpha <- 0.05 # set significance level # be sure function is loaded source("../hypo_2popproport.R") # run function hypoth_2test_prop( x_1, n_1, x_2, n_2, H_type, alpha ) ``` hypoth_2test_unknown() hypo_2unknown.R This script performs a test on H0: μ1 - μ2 = 0 against one of the standard alterntive hypotheses based on two samples, of size n_1 and n_2, that give us a sample means xbar_1 and xbar_2, and the sample standard deviations s_1 and s_2. We also need to specify the desired level of significance. Results are given for both the simple degrees of freedom and the computed degrees of freedom. Example: ```# set up problem n_1 <- 45 # sample 1 size xbar_1 <- 56.2 # sample 1 mean s_1 <- 4.32 # sample 1 std. dev. n_2 <- 58 # sample 2 size xbar_2 <- 57.9 # sample 2 mean s_2 <- 5.71 # sample 2 std. dev. # set up the type of test H_type <- -1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_2unknown.R") # run function hypoth_2test_unknown( s_1, n_1, xbar_1, s_2, n_2, xbar_2, H_type, alpha ) ``` hypoth_2test_var() hypo_2var.R This script performs a test on the equality of two population variances. The populations need to be normal. Arguments for the function include the sample sizes, n_top and n_bot, and the two sample standard deviations, s_top and s_bot. The type of the alternative hypothesis and the level of significance are also arguments. Example: ```# set up problem n_top <- 41 # size of sample in numerator s_top <- 7.8 # std. dev. of numerator sample n_bot <- 53 # size of sample in denominator s_bot <- 6.4 # std. dev. of denominator sample H_type <- -1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_2var.R") # run function hypoth_2test_var( n_top, s_top, n_bot, s_bot, H_type, alpha ) ``` hypoth_test_known() hypo_known.R This script performs a test on H0: μ = a against one of the standard alterntive hypotheses based on a sample of size n_1 that gives us a sample mean, xbar_1, and where we know the standard deviation, sigma_1, of the underlying population. We also need to specify the desired level of significance. Example: ```# set up problem sigma_1 <- 11.43 # population std. dev. n_1 <- 35 # sample size xbar_1 <- 74.6 # sample mean H0 <- 77.9 # null hypothesis value H_type <- -1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_known.R") # run function hypoth_test_known( H0, sigma_1, H_type, alpha, n_1, xbar_1) ``` hypoth_test_prop() hypo_prop.R This script performs a test on H0: p = a against one of the standard alterntive hypotheses based on a sample of size n_1 that gives us a count, x_1, of the items in the sample that display the characteristic of interest. We also need to specify the desired level of significance. Example: ```# set up problem n_1 <- 72 # sample size # number of items in the sample x_1 <- 28 # with the characteristic H0 <- 0.3 # null hypothesis value H_type <- 1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_prop.R") # run function hypoth_test_prop( H0, x_1, n_1, H_type, alpha ) ``` hypoth_test_sigma() hypo_sigma.R This script performs a test on H0: σ = a against one of the standard alterntive hypotheses based on a sample of size n_1 that gives us a sample standard deviation, s_1. We also need to specify the desired level of significance. The test should only be used if you are quite sure that the underlying population has a normal distribution. Example: ```# set up problem n_1 <- 72 # sample size s_1 <- 2.8 # sample standard deviation H0 <- 3.0 # null hypothesis value H_type <- -1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_sigma.R") # run function hypoth_test_sigma( H0, n_1, s_1, H_type, alpha ) ``` hypoth_test_unknown() hypo_unknown.R This script performs a test on H0: μ = a against one of the standard alterntive hypotheses based on a sample of size n_1 that gives us a sample mean, xbar_1, and where we do not know the standard deviation of the underlying population, but we do know the sample standard deviation, s_1. We also need to specify the desired level of significance. Example: ```# set up problem s_1 <- 11.43 # sample std. dev. n_1 <- 35 # sample size xbar_1 <- 74.6 # sample mean H0 <- 77.9 # null hypothesis value H_type <- -1 # neg for <, 0 for !=, pos for > alpha <- 0.05 # level of significance # make sure function is loaded source("../hypo_unknown.R") # run function hypoth_test_unknown( H0, H_type, alpha, n_1, xbar_1, s_1 ) ``` long_summary() long_summary.R This is an extension of the R function summary. This function gives all of the basic information but it augments that with the Q1 and Q3 values that would be computed by the TI-83/84 calculator. Furthermore, the long_summary function provides the size of the data list, the sum of the x's, the sum of the x² 's, the mean, the population standard deviation (sigma), and the sample standard deviation. Example: ```# set up problem L1 <- c(6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49) source("../long_summary.R") long_summary(L1) ``` make_freq_table() make_freq_table.R This script create a frequency table for given discrete data. Example: ```# set up problem # generate some values source("../gnrnd4.R") gnrnd4( 480933203,800025) L1 # look at those value # make sure function is loaded source("../make_freq_table.R") # run the function make_freq_table( L1 ) ``` Mode() mode.R Find the mode value or values in a set of values. Note that the function name starts with an upper case M. The function "mode() is defined in R but it has a different use. Example: ```# set up problem # generate some values source("../gnrnd4.R") gnrnd4( 490833203,800025) L1 # look at those value # make sure function is loaded source("../mode.R") # note lower case m # run the function Mode( L1 ) # note upper case M ``` model model.R This is not a function at all. This is a dummy file that I gave to students on their USB drive but which some of them have managed to delete. It is listed here so that students can save it to their USB dirive if need be. pbinomeq() pbinomeq.R This is a small function to find the probability of exactly one number, k, of successes in n trials with a probability of success given as p. Example: ```# set up problem n <- 14 # number of trials k <- 5 # number of successes p <- 0.32 # probability of success # make sure the functions are loaded source("../pbinomeq.R") # run the function pbinomeq( k, n, p ) ``` num_perm() nPr() permutations.R Functions to do permutations of n things taken r at a time. Example: ```# make sure the functions are loaded source("../permutations.R") # that actually loads two functions # num_perm() and nPr() # run both for 8 things taken 3 at a time num_perm( 8, 3 ) nPr( 8, 3 ) ``` pop_sd() pop_sd.R Computes the population standard devation given the raw data. Example: ```# set up problem # generate some values source("../gnrnd4.R") gnrnd4( 492833204,800035) L1 # look at those value # make sure function is loaded source("../pop_sd.R") # run the function pop_sd( L1 ) ``` pprop() pprop.R Computes the normal approximation for the probability of getting phat (or less) from a proportion with probability of success p and sample size n. Example: ```# set up problem # generate some values phat <- 0.37 # proportion in sample p <- 0.40 # proportion known in population n <- 32 # sample size # make sure function is loaded source("../pprop.R") # run the function # find prob of a sample # of size n with proportion # phat or less, if population pprop( phat, p, n ) # has proportion=p # same, but find probability # of phat or more pprop( phat, p, n, lower.tail=FALSE) ``` starter.R This file just contains comments. It is meant to be downloaded and then used as a starting point for an RStudio session. shuffle() shuffle.R This script creates a shuffled version of the list that is provided as the argument. Example: ```# set up problem L1 <- 1:100 # create a list of values 1 to 100 L1 # look at those value # make sure function is loaded source("../shuffle.R") # run the function shuffle( L1 ) # note that this does not change L1 L1 # to shuffle a list and have the list retain that shuffle L1 <- 1:100 L1 L1 <- shuffle( L1 ) # this changes the list L1 L1 ``` stem_leaf() stem_leaf.R This script creates a stem and leaf diagram of the data where the user specifie the data and the position of the cut between the stem and the leaf values. Example: ```# set up problem # generate some values source("../gnrnd4.R") gnrnd4( 492833204,600031) L1 # look at those value # make sure function is loaded source("../stem_leaf.R") # run the function stem_leaf( L1 ) ```