Question

Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. In a sample of 60 such students, the score on the second try was, on average, 30 points above the first try with a standard deviation of 14 points. Test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.05 significance level.(a) The claim is that the mean difference is greater than 25 (μd > 25), what type of test is this?1. This is a two-tailed test.2. This is a right-tailed test.3. This is a left-tailed test.(b) What is the test statistic? Round your answer to 2 decimal places.td= _______(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.P-value = _____(d) What is the conclusion regarding the null hypothesis?1. reject H02. fail to reject H0 (e) Choose the appropriate concluding statement.1. The data supports the claim that retaking the SAT increases the score on average by more than 25 points.2. There is not enough data to support the claim that retaking the SAT increases the score on average by more than 25 points. 3. We reject the claim that retaking the SAT increases the score on average by more than 25 points.4. We have proven that retaking the SAT increases the score on average by more than 25 points

Answer 1

what type of test is this?

2. This is a right-tailed test

(b) What is the test statistic?

`t=(\bar d -25)/((s_d)/(√(n)))=(30 -25)/((14)/(√(60)))=2.77`

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.P-value = _____

First we need to calculate the degrees of freedom given by:

`df=n-1=60-1=59`

Now we can calculate the p value, since we have a right tailed test the p value is given by:

`p_v =P(t_((59))>2.77) =0.0037`

And we can use the following excel code: "=1-T.DIST(2.77,59,TRUE)"

(d) What is the conclusion regarding the null hypothesis?1. reject H02. fail to reject H0

1. reject H0

e) Choose the appropriate concluding statement.

1. The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

Explanation:

Data given

`\bar X_d = 30` represent the sample mean difference

`s_d =14` represent the sample standard deviation

n=60 represent the sample size selected

`\alpha=0.05` represent the significance level

Confidence =1-0.05=0.95

System of Hypothesis

The system of hypothesis for this case are:

Null hypothesis:
`\mu_d \leq 25`

Alternative hypothesis:
`\mu_d >25`

what type of test is this?

2. This is a right-tailed test

(b) What is the test statistic?

`t=(\bar d -25)/((s_d)/(√(n)))=(30 -25)/((14)/(√(60)))=2.77`

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.P-value = _____

First we need to calculate the degrees of freedom given by:

`df=n-1=60-1=59`

Now we can calculate the p value, since we have a right tailed test the p value is given by:

`p_v =P(t_((59))>2.77) =0.0037`

And we can use the following excel code: "=1-T.DIST(2.77,59,TRUE)"

(d) What is the conclusion regarding the null hypothesis?1. reject H02. fail to reject H0

1. reject H0

e) Choose the appropriate concluding statement.

1. The data supports the claim that retaking the SAT increases the score on average by more than 25 points.