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.

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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. 

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Expert Answer

Step 1

Hypotheses:

Null hypothesis:

H0: µ =30

Alternative hypothesis:

H1: 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:

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Descriptive Statistics: Time Variable Mean StDev Time 28.00 3.71

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Step 2

The test statistics is ...

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28 30 3.71 -2 1.1732 =-1.705

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