The manager of The Cheesecake Factory in Boston would like t

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.

Solution

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