A random sample of 11 waiting times (in minutes) before patients saw a medical p

Question

A random sample of 11 waiting times (in minutes) before patients saw a medical professional in a hospital's minor emergency department had a standard deviation of 39.1 minutes. After a new admissions procedure was implemented, a random sample of 13 waiting times had a standard deviation of 31.3 minutes. At = 0.01, can you support the hospital's claim that the standard deviation of the waiting times has decreased? Complete parts (a) through (d) below (a) Identify the claim and state Ho and Ha. Let represent the initial variance and 2 represent the variance for the new process. Choose the correct answer below A, Ho: (claim) Ha : ng (claim) 2-2 (b) Calculate the test statistic. (Round to two decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis, and interpret the decision in the context of the claim. Can you support the hospital's claim? ( ( ( A. Fail to reject the null hypothesis. No, there is not enough evidence to support the claim. B. Fail to reject the null hypothesis. Yes, there is enough evidence to support the claim C. Reject the null hypothesis. Yes, there is enough evidence to support the claim D. Reject the null hypothesis. No, there is not enough evidence to support the claim

Explanation / Answer

The statistical software output for this problem is:

Two sample variance summary hypothesis test:
12 : Variance of population 1
22 : Variance of population 2
12/22 : Ratio of two variances
H0 : 12/22 = 1
HA : 12/22 < 1

Hypothesis test results:

Hence,

a) Hypotheses: Option C is correct.

b) Test statistic = 1.56

c) Option A is correct.

Ratio Num. DF Den. DF Sample Ratio F-Stat P-value 12/22 10 12 1.5605038 1.5605038 0.77

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