Question

A random sample of 37 second graders who participated in sports had manual dexterity scores with...

A random sample of 37 second graders who participated in sports had manual dexterity scores with mean 32.29 and standard deviation

4.14.

An independent sample of 37 second graders who did not participate in sports had manual dexterity scores with mean 31.88 and standard deviation

4.86.

(a)

Test to see whether sufficient evidence exists to indicate that second graders who participate in sports have a higher mean dexterity score. Use

α = 0.05.

State the null and alternative hypotheses. (Us

μ1

for students who participated in sports and

μ2

for students who did not participate in sports.)

H0: μ1μ2
Ha: μ1 = μ2

H0: μ1 = μ2
Ha: μ1 > μ2    

H0: μ1 = μ2
Ha: μ1 < μ2

H0: μ1 > μ2
Ha: μ1 = μ2

H0: μ1 = μ2
Ha: μ1μ2

State the rejection region. (Assume the test statistic will be calculated using students who participated in sports − students who did not participate in sports. Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

z> ___

z< ___

Calculate the appropriate test statistic. (Calculate the test statistic using students who participated in sports − students who did not participate in sports. Round your answer to two decimal places.)

z =

What is the conclusion of your test?

Reject H0. Sufficient evidence does not exist to indicate that second graders who participate in sports have a higher mean dexterity score.

Fail to reject H0. Sufficient evidence does not exist to indicate that second graders who participate in sports have a higher mean dexterity score.    

Fail to reject H0. Sufficient evidence exists to indicate that second graders who participate in sports have a higher mean dexterity score.

Reject H0. Sufficient evidence exists to indicate that second graders who participate in sports have a higher mean dexterity score.

(b)

For the rejection region used in part (a), calculate β when

μ1μ2 = 4.

(Round your answer to four decimal places.)

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