Question

Asked Nov 19, 2019

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Suppose a new director of health services for a district claims that she will reduce the average speed of emergency response to less than 30 minutes, which is thought to be the average response time with the current director. There are no past records so the actual standard deviation of such response times cannot be determined. Thanks to this promise, careful records are now kept. The response times for the first month are 26, 30, 28, 29, 25, 28, 32, 35, 24 and 23 minutes. Using the .05 level of significance, did she keep her promise? Explain your answer.

Step 1

**Hypotheses:**

*Null hypothesis:*

*H*_{0}: *µ* =30

*Alternative hypothesis:*

*H*_{1}: *µ* < 30

Since the alternative hypothesis states µ < 30, this test is a left-tailed test.

*Test statistic for t-test:*

Since population standard deviation is unknown, the appropriate test is one sample *t-*test.

*Test statistics:*

Step-by-step procedure to obtain the mean and standard deviation using MINITAB software:

- Choose
**Stat > Basic Statistics > Display Descriptive Statistics**. - In
**Variables**enter the columns**Time**. - Choose option
**statistics**, and select**Mean and standard deviation**. - Click
**OK**.

Output using the MINITAB software is given below:

Step 2

The test statistics is ...

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