10.2 Binomial Test

Hypothesis test about the probability of success.

Many government forms indicate the estimated time to fill out a form. This information can be used to calculate the (financial) burden associated with providing information to government agencies. For example, the instructions of the 2020 IRS Form 1040 state that the estimated average time burden for all taxpayers filing a Form 1040 or 1040-SR is 12 hours. Consider the data in irs which contains 40 observations of taxpayers filling out the form. Conducting a regular t-test leads to the rejection of the hypothesis:

The hypothesis is also rejected

In the sample, 16 observations are below the estimated 12 hours and 24 observations are above 12 hours.

binom.test(16,40)

## 
##  Exact binomial test
## 
## data:  16 and 40
## number of successes = 16, number of trials = 40, p-value = 0.2682
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2486500 0.5667329
## sample estimates:
## probability of success 
##                    0.4

checkout = c(3.8,5.3,3.5,4.5,7.2,5.1) t.test(checkout,mu=4,alternative=c(“greater”))