Question

A professor claims the Mallard grades for students average 93. He takes a random sample of 10 scores to test his claim—the scores are:

89

100

95

91

92

99

80

94

100

88

Assuming the grades are normally distributed, is there enough evidence to believe that the average is less than 93 at the .05 level of significance? (Round to 4 Decimal Places)

1. Is the test statistic for this test Z or t?

2. What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)

3. What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)

4. What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)

5. What decision should be made?

Select one:

a. Accept the null hypothesis

b. Reject the null hypothesis

c. Can not be determined from given information

d. Do not reject the null hypothesis

Answer 1

From the given sample ; n=19 , ,

The sample mean is ,

The sample standard deviation is ,

Hypothesis : VS  

1. Since , the population standard deviation is not known.

Therefore , use t-distribution.

df=degrees of freedom=n-1=10-1=9

2. The value of the test statistic is ,

3. The p-value is ,

The Excel fucntion is , =TDIST(0.1009,9,1)

4) The critical value is ,

; The Excel function is , =TINV(2*0.05,9)

5. Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , (b) Do not reject the null hypothesis.

Conclusion : Hence , there is not sufficient evidence to support the claim that the average is less than 93.