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 362 patients showed the mean wait time was 23.16 minutes, with a standard deviation of 16. 1 minutes. Complete parts (a) and (b) below. a. If you test the null hypothesis at the 0.05 level of significance, is there evidence that the population mean wait time is less than 25 minutes? State the null and alternative hypotheses. O A. Ho: p225 H:p*25 OD. Ho: #25 H:H2 25 B. Ho: 1225 H:H<25 E. Ho:<25 H: 1225 O C. Ho:u<25 H:> 25 OF. Ho: > 25 H:H<25 Find the test statistic for this hypothesis test. ESTAT = (Type an integer or a decimal. Round to two decimal places as needed.) Find the p-value. The p-value is (Type an integer or a decimal. Round to three decimal places as needed.) Is there sufficient evidence to reject the null hypothesis? (Use a 0.05 level of significance.) O A. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean wait time is less than 25 minutes. O B. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean wait time is greater than 25 minutes O C. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean wait time is greater than 25 minutes. OD. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean wait time is less than 25 minutes. b. Interpret the meaning of the p-value in this problem. Choose the correct answer below. O A. The p-value is the probability that the actual mean wait time is 25 minutes given the sample mean wait time is 23.16 minutes. OB. The p-value is the probability that the actual mean wait time is 23.16 minutes or less. O C. The p-value is the probability of getting a sample mean wait time of 23.16 minutes or less if the actual mean wait time is 25 minutes OD. The p-value is the probability that the actual mean wait time is more than 23.16 minutes.

Answer 1

3. IX = Given Population mean = 25 Given mean = 23.16 Standard deviation = 16.1 sample size = 362 Test hypothesis are Nullhypothesis Ho: 225 Alternate hypothesis H:< 25 (Option B Test statistic Test statistic t =(x-1)/(s/n) = (23.16-25)/(16.1/sqrt(25)) = -2.174 P-value P(t<-0.571) = 0.0152 (Left tailed) Since p-value <0.05 hence fail to reject the null hypothesis Option A is corret Interpret the meanng of the p-value The p-value is the prebability of getting a sample mean weght time of 23.16 minutes or less if the acual mean time is 25 minutes Option C is correct