Problem Page

Question

Over the years, themeancustomer satisfaction rating at a local restaurant has been

79

.The restaurant was recently remodeled, and now the management claims the mean customer rating,

,is not equal to

79

.In a sample of

51

customerschosen at random, the mean customer rating is

81.2

.Assume that thepopulation standard deviationof customer ratings is

7.5

.

Is there enough evidence to support the claim that the mean customer rating is different from

79

? Perform ahypothesis test, using the

0.10

level of significance.

(a)State thenull hypothesis

H0

and thealternative hypothesis

H1

.

H0 :
H1 :

(b)Perform a

Z

-testand find thep-value. Here is some information to help you with your

Z

-test.

• The value of thetest statisticis given by
• Thep-valueis two times the area under the curve to the right of the value of the test statistic.

Standard Normal Distribution

Step 1: Select one-tailed or two-tailed.

One-tailed

Two-tailed

Step 2: Enter the test statistic. (Round to 3 decimal places.)

Step 3: Shade the area represented by thep-value.

Step 4: Enter thep-value. (Round to 3 decimal places.)

0.1

0.2

0.3

0.4

1

1

2

2

3

3

(c)Based on your answer to part (b), choose what can be concluded, at the

0.10

level of significance, about the claim made by the management.

Since thep-valueis less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean customer rating is not equal to 79 . Since thep-valueis less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there isnotenough evidence to support the claim that the mean customer rating is not equal to 79 . Since thep-valueis greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean customer rating is not equal to 79 . Since thep-valueis greater than the level of significance, the null hypothesis is not rejected. So, there isnotenough evidence to support the claim that the mean customer rating is not equal to 79 .

Clears your work.

Undoes your last action.

Provides information about entering answers.

Tool to shade regions under a curve

xn

• .