Question

**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 a right-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

a).This is a two-tailed test

hypothesis:-

H₀: μ = 505 |

H₁: μ ≠ 505 |

b).given,

**c).p
value:-**

for df= 60-1 = 59, los 10%, p value=**0.2021**

[from p value calculator from t]

d). the conclusion regarding the null hypothesis be:-

**fail to reject
H_{0}** [ as the p value = 0.2021
< 0.10]

e).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**

***If you have any doubt regarding the problem please write it in the comment section.if you are satisfied please give me a LIKE if possible...

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