The manager of The Cheesecake Factory in Boston would like to know the mean numb

Question

The manager of The Cheesecake Factory in Boston would like to know the mean number of customers served on weekdays. She believes that the number of customers served follows a Normal distribution. She reports that on six randomly selected weekdays an average of 158.3 customers were served with a sample standard deviation of 52.2.

a. Calculate the standard error of the sample mean.

b. Find the number of degrees of freedom for a sample of n = 6.

c. Find the t-critical value for a 99% confidence interval.

d. Calculate a 99% confidence interval of the mean.

e. Interpret the confidence interval in the context of the problem.

Explanation / Answer

a.) Std error = 52.2/6. = 21.31

b.) Degrees of freedom = n -1= 5

c.) Critical value = t0.005 = 4.0322

d.) 99% confidence imterval for mean is

( 158.3 - 4.0322 × 21.31 , 158.3 + 4.0322 × 21.31)

(72.37 , 244.23)

e.) The mean number of customers served per day is in the interval 72.37 to 244.23, 99% of the times

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