Question

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

*μ*_{1}

for students who participated in sports and

*μ*_{2}

for students who did not participate in sports.)

*H*_{0}: *μ*_{1} ≠
*μ*_{2}

*H*_{a}: *μ*_{1} =
*μ*_{2}

*H*_{0}: *μ*_{1} =
*μ*_{2}

*H*_{a}: *μ*_{1} >
*μ*_{2}

*H*_{0}: *μ*_{1} =
*μ*_{2}

*H*_{a}: *μ*_{1} <
*μ*_{2}

*H*_{0}: *μ*_{1} >
*μ*_{2}

*H*_{a}: *μ*_{1} =
*μ*_{2}

*H*_{0}: *μ*_{1} =
*μ*_{2}

*H*_{a}: *μ*_{1} ≠
*μ*_{2}

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 *H*_{0}. Sufficient evidence does
not exist to indicate that second graders who participate in sports
have a higher mean dexterity score.

Fail to reject *H*_{0}. Sufficient
evidence does not exist to indicate that second graders who
participate in sports have a higher mean dexterity
score.

Fail to reject *H*_{0}. Sufficient
evidence exists to indicate that second graders who participate in
sports have a higher mean dexterity score.

Reject *H*_{0}. 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

*μ*_{1} − *μ*_{2} = 4.

(Round your answer to four decimal places.)

Answer #1

I have given my best to solve your problem. Please like the answer if you are satisfied with it. ?

The College Board provided comparisons of Scholastic Aptitude
Test (SAT) scores based on the highest level of education attained
by the test taker's parents. A research hypothesis was that
students whose parents had attained a higher level of education
would on average score higher on the SAT. The overall mean SAT math
score was 514.† SAT math scores for independent samples of students
follow. The first sample shows the SAT math test scores for
students whose parents are college graduates...

The College Board provided comparisons of Scholastic Aptitude
Test (SAT) scores based on the highest level of education attained
by the test taker's parents. A research hypothesis was that
students whose parents had attained a higher level of education
would on average score higher on the SAT. The overall mean SAT math
score was 514.† SAT math scores for independent samples of students
follow. The first sample shows the SAT math test scores for
students whose parents are college graduates...

You may need to use the appropriate technology to answer this
question.
The College Board provided comparisons of Scholastic Aptitude
Test (SAT) scores based on the highest level of education attained
by the test taker's parents. A research hypothesis was that
students whose parents had attained a higher level of education
would on average score higher on the SAT. The overall mean SAT math
score was 514.† SAT math scores for independent samples of students
follow. The first sample shows...

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The College Board provided comparisons of Scholastic Aptitude
Test (SAT) scores based on the highest level of education attained
by the test taker's parents. A research hypothesis was that
students whose parents had attained a higher level of education
would on average score higher on the SAT. The overall mean SAT math
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students whose parents are college graduates...

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