Question

QSR magazine assessed the work of McDonalds and Taco Time restaurants in terms of their service time in seconds. For the sample of 308 observations from Taco Time restaurants, the mean service time was 158.03 seconds with a standard deviation of 33.8 seconds. For the sample of 317 observations from McDonalds restaurants, the mean service time was 189.49 seconds with a standard deviation of 41.3 seconds. Construct a 95% confidence interval.

Answer 1

Let the mean service time of McDonalds and Taco Time restaurant be and respectively.

The data given in the question are summarized as follows:

Statistic	Sample 1	Sample 2
Sample size	n1=317	n2=308
Sample mean	=189.49	=158.03
Sample SD	s1=41.3	s2=33.8

The 95% confidence interval is given by

where s' is given by

The critical value is obtained from the Biometrika table as

Now the 95% confidence interval is given by

Hence the 95% confidence interval is given by

(25.53381122,37.38618878)

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