Question

Suppose the national mean SAT score in mathematics was 515. In a random sample of 40 graduates from Stevens High, the mean SAT score in math was 507, with a standard deviation of 30. Test the claim that the mean SAT score for Stevens High graduates is the same as the national average. Test this claim at the 0.05 significance level.

(a) What type of test is this?

This is a left-tailed test.

This is a right-tailed test.

This is a two-tailed test.

(b) What is the test statistic? **Round your answer to 2
decimal places.**

*t*_{x} =

(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?

reject *H*_{0}

fail to reject
*H*_{0}

(e) Choose the appropriate concluding statement.

There is enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average.

There is not enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average.

We have proven that the mean math SAT score for Stevens High graduates is the same as the national average.

Answer #1

Suppose the national mean SAT score in mathematics was 510. In a
random sample of 40 graduates from Stevens High, the mean SAT score
in math was 501, with a standard deviation of 40. Test the claim
that the mean SAT score for Stevens High graduates is the same as
the national average. Test this claim at the 0.10 significance
level. (a) What type of test is this? This is a two-tailed test.
This is a right-tailed test. This is...

Math SAT: Suppose the national mean SAT score
in mathematics was 505. In a random sample of 40 graduates from
Stevens High, the mean SAT score in math was 495, with a standard
deviation of 30. Test the claim that the mean SAT score for Stevens
High graduates is the same as the national average. Test this claim
at the 0.01 significance level.
(a) What type of test is this?
This is a left-tailed test.
This is a right-tailed test. ...

Math SAT: Suppose the national mean SAT score
in mathematics was 505. In a random sample of 50 graduates from
Stevens High, the mean SAT score in math was 495, with a standard
deviation of 30. Test the claim that the mean SAT score for Stevens
High graduates is the same as the national average. Test this claim
at the 0.05 significance level.
(a) What type of test is this?
This is a two-tailed test. This is a left-tailed
test. ...

Math SAT: Suppose the national mean SAT score
in mathematics was 505. In a random sample of 60 graduates from
Stevens High, the mean SAT score in math was 510, with a standard
deviation of 30. Test the claim that the mean SAT score for Stevens
High graduates is the same as the national average. Test this claim
at the 0.10 significance level.
(a) What type of test is this?
This is a left-tailed test.This is a two-tailed
test. This is...

Math SAT: The math SAT test was originally
designed to have a mean of 500 and a standard deviation of 100. The
mean math SAT score last year was 515 but the standard deviation
was not reported. You read in an article for an SAT prep course
that states in a sample of 75 students, the mean math score was
546, but they did not disclose the standard deviation. Assume the
population standard deviation (σ) for all prep course
students...

Math SAT: The math SAT test was originally
designed to have a mean of 500 and a standard deviation of 100. The
mean math SAT score last year was 515 but the standard deviation
was not reported. You read in an article for an SAT prep course
that states in a sample of 87 students, the mean math score was
534, but they did not disclose the standard deviation. Assume the
population standard deviation (σ) for all prep course
students...

Suppose that the national average for the math portion of the
College Board's SAT is 515. The College Board periodically rescales
the test scores such that the standard deviation is approximately
100. Answer the following questions using a bell-shaped
distribution and the empirical rule for the math test scores.
If required, round your answers to two decimal places. If your
answer is negative use “minus sign”.
(a)
What percentage of students have an SAT math score greater than
615?
(b)...

Retaking the SAT: Many high school students
take the SAT's twice; once in their Junior year and once in their
Senior year. In a sample of 55 such students, the score on the
second try was, on average, 34 points above the first try with a
standard deviation of 15 points. Test the claim that retaking the
SAT increases the score on average by more than 30 points. Test
this claim at the 0.10 significance level.
(a) The claim is...

Retaking the SAT: Many high school students
take the SAT's twice; once in their Junior year and once in their
Senior year. In a sample of 55 such students, the score on the
second try was, on average, 33 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 30 points. Test
this claim at the 0.01 significance level.
(a) The claim is...

Retaking the SAT: Many high school students
take the SAT's twice; once in their Junior year and once in their
Senior year. In a sample of 50 such students, the score on the
second try was, on average, 35 points above the first try with a
standard deviation of 13 points. Test the claim that retaking the
SAT increases the score on average by more than 30 points. Test
this claim at the 0.05 significance level.
(a) The claim is...

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