Question

A hospital was concerned about reducing its wait time. A targeted wait time goal of 25 minutes was set. After implementing an improvement framework and? process, a sample of 364 patients showed the mean wait time was 23.06 ?minutes, with a standard deviation of 16.4 minutes. Complete parts? (a) and? (b) below. a. If you test the null hypothesis at the 0.10 level of? significance, is there evidence that the population mean wait time is less than 25 ?minutes? State the null and alternative hypotheses. A. Upper H 0?: mu greater than 25 Upper H 1?: mu less than 25 B. Upper H 0?: mu not equals 25 Upper H 1?: mu greater than or equals 25 C. Upper H 0?: mu greater than or equals 25 Upper H 1?: mu less than 25 D. Upper H 0?: mu greater than or equals 25 Upper H 1?: mu not equals 25 E. Upper H 0?: mu less than 25 Upper H 1?: mu greater than 25 F. Upper H 0?: mu less than 25 Upper H 1?: mu greater than or equals 25 Find the test statistic for this hypothesis test. t Subscript STATequals nothing ?(Type an integer or a decimal. Round to two decimal places as? needed.) Find the? p-value. The? p-value is nothing. ?(Type an integer or a decimal. Round to three decimal places as? needed.) Is there sufficient evidence to reject the null? hypothesis? (Use a 0.10 level of? significance.) A. Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean wait time is less than 25 minutes. B. Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean wait time is less than 25 minutes. C. Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean wait time is greater than 25 minutes. D. Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean wait time is greater than 25 minutes. b. Interpret the meaning of the? p-value in this problem. Choose the correct answer below. A. The? p-value is the probability that the actual mean wait time is 25 minutes given the sample mean wait time is 23.06 minutes. B. The? p-value is the probability of getting a sample mean wait time of 23.06 minutes or less if the actual mean wait time is 25 minutes. C. The? p-value is the probability that the actual mean wait time is more than 23.06 minutes. D. The? p-value is the probability that the actual mean wait time is 23.06 minutes or less.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H₀ : ? = 25
H_A : ? < 25

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
?	23.06	0.85959357	363	-2.2568805	0.0123

Hence,

a) Hypotheses:

Ho: ? = 25

Ha: ? < 25

t_STAT = -2.26

p - Value = 0.012

Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean wait time is less than 25 minutes. Option B is correct.

The? p-value is the probability of getting a sample mean wait time of 23.06 minutes or less if the actual mean wait time is 25 minutes. Option B is correct.