A college indicates that, on average, graduating students achieve a GPA of at most 2.1 from their science programs. The board of Governors commissions a study to verify this information. A random sample of 10 graduate student's GPAs is taken and the following results are obtained. Assume that student's GPAs are normally distributed:

2.3, 2.7, 2.9, 3.2, 2.4, 2.1, 2.4, 2.3, 2.3, 2.7.

At a 0.01 significance level, test the hypothesis that the average GPA of graduating students is more than 2.1.

a)Identify the null hypothesis and alternative hypothesis.H₀: 2.1

H₁: > 2.1.H₀: = 2.1

H₁: < 2.1.H₀: = 2.1

H₁: 2.1.None of the above

b)State the critical value.

For full marks your answer should be accurate to at least three decimal places.

Critical value:

0

c)Determine the value of the test statistic.

For full marks your answer should be accurate to at least three decimal places.

Test statistic:

0

d)Identify the correct interpretation.Since the test statistic is in the rejection region, rejectH₀and acceptH₁.Since the test statistic is in the rejection region, do not rejectH₀.Since the test statistic isnotin the rejection region, rejectH₀and acceptH₁.Since the test statistic isnotin the rejection region, do not rejectH₀.

e)What conclusion can be drawn from the interpretation at 0.01 significance level?There isnotenough statistical evidence that the GPA is different than 2.1.There is significant evidence that the GPA is different than 2.1.There isnotenough statistical evidence that the GPA is more than 2.1.There is significant evidence that the GPA is more than 2.1.There isnotenough statistical evidence that the GPA is less than 2.1.There is significant evidence that the GPA is less than 2.1.