Question

10. Suppose a new Director of HealthServicesfor 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. Do not show full working steps.

Answer 1

$\bar x=28, \;\;s=3.71.$

One sample t-test should be used.

Null hypothesis $H_0:\;\mu=30.$

Alternative hypothesis $H_a:\;\mu<30.$

Test statistic: $t=\frac{\bar x-\mu}{\frac{s}{\sqrt{n}}}=-1.70.$

Degrees of freedom: $df=10-1=9.$

P-value (from t-table): $p=0.061.$

Since P-value is greater than 0.05, fail to reject the null hypothesis.

She did not keep her promise.