A luxury retailer requires that customers receive personal attention from sales

Question

A luxury retailer requires that customers receive personal attention from sales associates within 5 min of entering a store. To test for adherence to policy, an analyst from the corporate office defined a null hypothesis, H0:=5 min, reflecting company policy on customer wait times, and formulated an alternative hypothesis, H1:>5 min, to indicate that customer wait times exceeded 5 min, on average. A sample of 10 customers’ wait times revealed a sample standard deviation of 1.75 min. The analyst collected data for this sample at regular intervals, and experience has shown that this procedure gives data that can be treated as random samples from a normal population. Because of the small sample size, the analyst chose to use a one-sample ttest.

Determine the minimum value for mean wait time which, if observed in the sample, would lead the analyst to reject the null hypothesis at an alpha level of 0.05. Report results in minutes to three decimal places.

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =0.5534

for 9 degree of freedom and 0.05 level for one tailed test ; critical value of t =1.833

hence  minimum value for mean wait time which, if observed in the sample, would lead the analyst to reject the null hypothesis =5+1.833*0.5534=6.014

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