Question

Student's t Distribution CI (PLEASE SHOW EXCEL FUNCTIONS)

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.

(EXCEL FUNCTIONS)

a. Calculate the standard error of the sample mean. (EXCEL FUNCTIONS)
b. Find the t-critical value for a 99% confidence interval with a sample size of 6. (EXCEL FUNCTIONS)
c. Calculate a 99% confidence interval of the mean. (EXCEL FUNCTIONS)
d. Interpret the confidence interval in the context of the problem. (EXCEL FUNCTIONS)

Answer 1

excel function are in bold:

a)

std error 'sx=s/√n=52.2/sqrt(6)=

21.3106

b)

for 99% CI; and 5 df, value of t=tinv(1-0.99,6-1) =4.032

c)

margin of error E=t*std error    =4.032*21.3106 =		85.924
lower bound=sample mean-E =158.3-85.924 =		72.376
Upper bound=sample mean+E =158.3+85.924 =		244.224

from above 99% confidence interval for population mean =(72.38,244.22)

d)

above interval gives 99% confidence to contain true value of population mean