Question

At the time she was hired, as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average more than $82 a day in tips." Over the first 15 days she was employed at the restaurant, the mean daily amount of her tips was $80.80, with a standard deviation of $4.50. At the 0.01 significance level, can Ms. Brigden conclude that she is earning an average of less than $82 in tips? Question: Put the data, State the hypotheses, and calculate the test statistic (only). Note: Provide the requested answers only.

Answer 1

(1)Given Data

Sample mean X= 80.80$

Sample standard deviation s = 4.50$,

Sample size n = 15 days

Degree of Freedom = df = 15-1 = 14

Significance level = α=0.01

(2) Null and Alternative hypothesis

The following Null and Alternative hypothesis need to be tested:

Ho: µ = 82

Ha: µ < 82

This corresponds to a left-tailed test, for which a t-test will be done since sample standard  deviation is given.

(3) Test statistics

The t-statistic is computed as follows

The p-value is calculated as p = 0.1596,

using Excel formula =T.DIST(-1.033,14,TRUE)

Note - Provided only answer you asked for, Thanks

We were unable to transcribe this image

t 80.80 – 82 4.50 V15

We were unable to transcribe this image