Lab 11 Solution

Submit an HTML document by the beginning of class.


Exercise

Now that we’re officially equipped with IF-statements, let’s create a more robust and powerful hypothesis test function!

Your task is to write a function hyp_test which performs a one-sample hypothesis test about either a mean or a proportion. Your function should take the following arguments:

    • data - a vector of numeric or factor values (this is the sample of data). This sample can have missing (NA) values in it. If numeric, the function will perform a one-sample t-test for a mean. If factor, the function will perform a one-sample z-test for a proportion. For a z-test, the sample proportion will be the proportion of data in the first factor level.

    • null - a single numeric value (this is the hypothesized value).

    • alpha - a single numeric value (this is the significance level). This should default to 0.05.

    • alternative - a character string specifying the form of the alternative hypothsis (“less”, “greater”, “two-sided”). This should default to “two-sided”.

Value

Your function should ignore any missing values in the data and return a list with the following components:

    • statistic : the value of the z- or t-statistic

    • df : degrees of freedom if appropriate

    • p.value : the p-value for the test

    • conf.int : a confidence interval for the proportion (or mean) appropriate to the specified alpha

    • estimate : the estimated proportion (or mean) based on the data

    • null.value : the specified hypothesized value of the proportion (or mean)

    • alpha : the specified significance level

Display

Besides returning the items listed above, your function should print the following:

    • The null hypothesis

    • The value of the test statistic and the p-value

    • The confidence interval for the proportion (or mean)





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NOTE 1: Your function should perform a check to make sure the null hypothesis value is between 0 and 1 for the one proportion test; otherwise, your function should return an error.


NOTE 2: You may NOT use R’s t.test() except to check your work.


Example

Test your code in AT LEAST the following 5 ways.

#TEST 1


data <- c(NA, 5:25)

hyp_test(data, null = 16, alpha = .05, alternative = "two-sided")

    • Ho: mu = 16

    • Test Statistic: -0.74 , p-value: 0.4688

    • Confidence Interval: (12.18,17.82)

    • $statistic

    • [1] -0.7385489

##

    • $df

    • [1] 20

    • 

    • $p.value

    • [1] 0.4687599

    • 

    • $conf.int

    • [1] 12.17559 17.82441

    • 

    • $estimate

    • [1] 15

##

    • $null.value

    • [1] 16

##

    • $alpha

    • [1] 0.05

#TEST 2


data <- factor(c(NA, rep("a", 60), rep("b", 40)))

hyp_test(data, null = .5, alpha = .01, alternative = "greater")

    • Ho: p = 0.5

    • Test Statistic: 2 , p-value: 0.0228

    • Confidence Interval: (0.4738,0.7262)

    • $statistic

    • [1] 2

##

    • $p.value

    • [1] 0.02275013

    • 


2
    • $conf.int

    • [1] 0.4738107 0.7261893

    • 

    • $estimate

    • [1] 0.6

##

    • $null.value

    • [1] 0.5

##

    • $alpha

    • [1] 0.01

    • TEST 3


data <- factor(c(NA, rep("a", 60), rep("b", 40)))

hyp_test(data, null = 1.4, alpha = .01, alternative = "greater")

    • Error: invalid hypothesized value. Must be between 0 and 1

    • [1] NA

    • TEST 4


data <- 1:10

hyp_test(data, null = 6, alpha = .101, alternative = "greater")

    • Ho: mu = 6

    • Test Statistic: -0.52 , p-value: 0.6929

    • Confidence Interval: (3.75,7.25)

    • $statistic

    • [1] -0.522233

##

    • $df

    • [1] 9

    • 

    • $p.value

    • [1] 0.6929414

    • 

    • $conf.int

    • [1] 3.750928 7.249072

    • 

    • $estimate

    • [1] 5.5

##

    • $null.value

    • [1] 6

##

    • $alpha

    • [1] 0.101

    • TEST 5


data <- factor(c(NA, rep("a", 60), rep("b", 40)))

hyp_test(data, null = 0.70, alpha = .02, alternative = "less")

    • Ho: p = 0.7

    • Test Statistic: -2.18 , p-value: 0.0145



3
    • Confidence Interval: (0.486,0.714)

    • $statistic

    • [1] -2.182179

##

    • $p.value

    • [1] 0.01454817

    • 

    • $conf.int

    • [1] 0.4860327 0.7139673

    • 

    • $estimate

    • [1] 0.6

##

    • $null.value

    • [1] 0.7

##

    • $alpha

    • [1] 0.02












































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