Question

Determine the critical value(s) of the test statistic for each of the following small sample tests for the population mean where the assumption of normality is satisfied. Round your answer to four decimal places.

Left-tailed test,α=0.01,n=24

Right-tailed test ,α=0.1,n=8

Two-tailed test, α=0.05,n=12

A high school principle currently encourages students to enroll in a specific SAT prep program that has a reputation of improving score by 50 points on average. A new SAT prep program has been released and claims to be better than their current program. The principle is thinking of advertising this new program to students if there is enough evidence at the 5% level that their claim is true. The principle tests the following hypotheses:

H0:μ=50 points

HA:μ>50 points

where μμ is the true mean in difference of scores after the new SAT prep course is taken and before the new SAT prep course is taken. He randomly assigns 93 students to take this new SAT program. The difference in scores resulted in an average of 50.3364 points with a standard deviation of 13.0174 points.

What is the value of the test statistic for this test? Round your answer to four decimal places.

What is your decision regarding the null hypothesis?

A. Reject the null hypothesis, at the 5% significance level, there is not enough evidence to say that the new SAT prep program is better than the current SAT prep program.

B. Fail to reject the null hypothesis, at the 5% significance level, there is not enough evidence to say that the new SAT prep program is better than the current SAT prep program.

C. Fail to reject the null hypothesis, at the 5% significance level, there is enough evidence to say that the new SAT prep program is better than the current SAT prep program.

D. Reject the null hypothesis, at the 5% significance level, there is enough evidence to say that the new SAT prep program is better than the current SAT prep program.

The average height of men in 1960 was found to be 68 inches (5 feet, 8 inches). A researcher claims that men today are taller than they were in 1960 and would like to test this hypothesis at the 0.01 significance level. The researcher randomly selects 184 men and records their height to find an average of 69.7020 inches with standard deviation of 1.1125 inches.

What is the value of the test statistic? Round your answer to four decimal places.

What is your decision regarding the null hypothesis?

A. Fail to reject the null hypothesis. At the 1% significance level there is not sufficient evidence to say that men today are taller than they were in 1960.

B. Fail to reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

C. Reject the null hypothesis. At the 1% significance level there is not sufficient evidence to say that men today are taller than they were in 1960.

D. Reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

Answer 1

We use t-test for small sample when the normality assumption is satisfied.

Left-tailed test, α=0.01,n=24 :

Degree of freedom, df = n - 1 = 24 - 1 =23

The t-critical value for a left-tailed test, for a significance level of α=0.01 and df = 23 is

t_c = 2.5000

Right-tailed test ,α=0.1,n=8

Degree of freedom, df = n - 1 = 8 - 1 =7

The t-critical value for a right-tailed test, for a significance level of α=0.1 and df = 7 is

t_c = 1.4149

Two-tailed test, α=0.05,n=12

Degree of freedom, df = n - 1 = 12 - 1 =11

The t-critical value for a two-tailed test, for a significance level of α=0.05 and df =11 is

t_c = 2.2010