According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assisterto answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callerswho placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting timeof 11 minutes before an IRS telephone assister answers. Based on data from past years, you decide that it isreasonable to assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can youconclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day issignificantly less than the overall mean waiting time of 13 minutes? Use a = 0.05.State the hypotheses.Ho:13Ha: < 13What is the p-value (to 4 decimals)?0.0217Can you conclude that callers who use the IRS help-line early in the day have a shorter wait?No

The hypothesized average waiting time for calls, μ0=13.The sample size, i.e., the sampled number of calls that are placed on the first 30 minutes, n=50.The sample average wait time for calls, x¯=11.The population standard deviation for the distribution of the wait time (in minutes), σ=8.Considering μ as the average waiting time during the first 30 minutes on the IRS helpline, it is set up as follows:H0:μ≥13; the average waiting time during the first 30 minutes on the IRS helpline is hypothesized to be not less than the overall average wait time of 13 minutes.H1:μ<13; the average waiting time during the first 30 minutes on the IRS helpline is hypothesized to be less than the overall average wait time of 13 minutes.The test statistic is:z=x¯−μ0σn=11−13850≈−1.768The p-value (left-tailed) for the z-score of −1.768 is obtained using the excel function "NORM.S.DIST(z,cumulative)" as follows:The p-value is 0.0385.The decision rule is: "reject H0, if p-value≤α".For α=0.05, p-value (=0.0385)<α. Thus H0 is rejected.The average waiting time during the first 30 minutes on the IRS helpline is hypothesized to be less than the overall average wait time of 13 minutes.The hypotheses are: H0:μ≥13; H1:μ<13.The p-value is 0.0385.Yes, it can be concluded that callers who use the IRS help-line early in the day have a shorter wait.