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A random sample of 15 observations from the first population revealed a sample m

ID: 3309518 • Letter: A

Question

A random sample of 15 observations from the first population revealed a sample mean of 314 and a sample standard deviation of 13. A random sample of 21 observations from the second population revealed a sample mean of 302 and a sample standard deviation of 10.

At the 0.05 significance level, is there a difference in the population means?

State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.)

Compute the pooled estimate of the population variance. (Round the final answer to 2 decimal places.)

The null and alternate hypotheses are:

Explanation / Answer

Result:

The null and alternate hypotheses are:

A random sample of 15 observations from the first population revealed a sample mean of 314 and a sample standard deviation of 13. A random sample of 21 observations from the second population revealed a sample mean of 302 and a sample standard deviation of 10.

At the 0.05 significance level, is there a difference in the population means?

a.

State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.)

          

The decision rule is to reject H0 if t < -2.032  or >2.032 .

This is a (Click to select)two tailed test.

b.

Compute the pooled estimate of the population variance. (Round the final answer to 2 decimal places.)

          

Pooled estimate of the population variance 128.41

c.

Compute the test statistic. (Round the final answer to 3 decimal places.)

           

The test statistic is: t = 3.132.

d.

What is your decision regarding H0?

             

H0 is (Click to select) rejected.

e.

Estimate the p-value. (Round the final answer to 4 decimal places.)

            

The p-value is 0.0036 .

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

15

Sample Mean

314

Sample Standard Deviation

13

Population 2 Sample

Sample Size

21

Sample Mean

302

Sample Standard Deviation

10

Intermediate Calculations

Population 1 Sample Degrees of Freedom

14

Population 2 Sample Degrees of Freedom

20

Total Degrees of Freedom

34

Pooled Variance

128.4118

Standard Error

3.8309

Difference in Sample Means

12.0000

t Test Statistic

3.1324

Two-Tail Test

Lower Critical Value

-2.0322

Upper Critical Value

2.0322

p-Value

0.0036

Reject the null hypothesis

The null and alternate hypotheses are:

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