Question

study of 100 students in a local university gave the average GPA to be 3.1 with a standard deviation of.5. The same study revealed that in this sample, 20% are out of state students.

Question 1

100 students, the critical value at alpha=.06, to test the hypothesis that the true mean GPA is different from 3.0 is............. , while the test statistic value, correct up to 2 decimal places is.................

Question 2

the same study with 100 students, the critical value at alpha=.06, to test the hypothesis that the true mean GPA is more than 3.0 is......

........ , while the test statistic value, correct up to 2 decimal places is............

Useful key words (phrases) are: parameter of interest, one tailed or two tailed, large or small sample, df

Question 3

lower bound, correct up to 3 decimal places, of a 95% confidence interval for the true GPA with a sample size of 20, a sample mean of 3.1 ad a standard deviation of 0.5 is

Question 4

lower bound, correct up to 3 decimal places of a 90% confidence interval for the true proportion of out of state students is

Answer 1

1)

Answer:

Critical values = -1.9026, 1.9026

t statistic = 2

Explanation: Since the population standard deviation is known, the t distribution is used to test the hypothesis.

The critical value for the t statistic is obtained in excel using the function =T.INV.2T(0.06,99) for significance level = 0.06, degree of freedom = n-1=100-1=99 and for a two-tailed test.

The t statistic is obtained using the following formula,

2)

Answer:

Critical values = 1.5683

t statistic = 2

Explanation:

This is a right-tailed test.

The critical value for the t statistic is obtained in excel using the function =T.INV(0.94,99) for significance level = 0.06, degree of freedom = n-1=100-1=99 and for a one-tailed test.

The t statistic is obtained using the following formula,

3)

Answer:

Explanation:

The lower bound for the 95% CI is obtained using the following formula,

The critical value for the t statistic is obtained in excel using the function =T.INV(0.025,99) for significance level = 0.06, degree of freedom = n-1=100-1=99

4)

Answer:

​​​​​​​

Explanation:

The lower bound for the 90% CI of the proportion of out of State students is obtained using the following formula,

The critical value for the z statistic is obtained in excel using the function =NORM.S.INV(0.025,99) for significance level = 0.06, degree of freedom = n-1=100-1=99

sample size, n = 100