g 2) For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with an average score of 500 for all U.S. students. The dean of students of Ross College suspects that in recent years the college has attracted students who are more quantitatively inclined. A random sample of 350 students entering Ross College had an average SAT Math (SAT-M) score of 510, and a sample standard deviation of 125. Does this provide enough evidence for the dean to conclude that the mean SAT-M score of all Ross College students is higher than the national mean?

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11-05-2020
Mathematics

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g 2) For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with an average score of 500 for all U.S. students. The dean of students of Ross College suspects that in recent years the college has attracted students who are more quantitatively inclined. A random sample of 350 students entering Ross College had an average SAT Math (SAT-M) score of 510, and a sample standard deviation of 125. Does this provide enough evidence for the dean to conclude that the mean SAT-M score of all Ross College students is higher than the national mean?

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mtosi17 mtosi17 · Answer 1 · 2020-05-19T04:40:30+02:00

Answer:

No. There is not enough evidence to support the claim that the mean SAT-M score of all Ross College students is higher than the national mean (P-value: 0.068) .

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean SAT-M score of all Ross College students is higher than the national mean .

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=500\\\\H_a:\mu> 500[/tex]

The significance level is 0.05.

The sample has a size n=350.

The sample mean is M=510.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=125.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{125}{\sqrt{350}}=6.682[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{510-500}{6.682}=\dfrac{10}{6.682}=1.497[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=350-1=349[/tex]

This test is a right-tailed test, with 349 degrees of freedom and t=1.497, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>1.497)=0.068[/tex]

As the P-value (0.068) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean SAT-M score of all Ross College students is higher than the national mean .

ahirohit963 ahirohit963 · Answer 2 · 2021-11-24T06:43:34+01:00

The null hypothesis is failed to be rejected. There is not enough evidence to support the claim that the mean SAT-M score of all Ross College students is higher than the national mean.

Given :

For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with an average score of 500 for all U.S. students.
A random sample of 350 students entering Ross College had an average SAT Math (SAT-M) score of 510, and a sample standard deviation of 125.

This problem is done by using the Hypothesis test for the population mean. The null and alternative hypotheses are:

[tex]\rm H_0 :\mu = 500\\[/tex]

[tex]\rm H_1 : \mu >500[/tex]

Given that the Significance level is 0.05, sample size n is 350, and the sample mean M is 510.

The standard deviation of the population is not given, so estimate it with the sample standard deviation, s = 125.

The estimated standard error of the mean is:

[tex]\rm s_M = \dfrac{s}{\sqrt{n} }[/tex]

[tex]\rm s_M = \dfrac{125}{\sqrt{350} } = 6.682[/tex]

Now, the t statistics are given by:

[tex]\rm t =\dfrac{M-\mu}{s/\sqrt{n} }[/tex]

[tex]\rm t =\dfrac{510-500}{6.682}=1.497[/tex]

The degree of freedom is given by:

df = n - 1 = 350 - 1 = 349

The P-value is given by:

P value = P(t > 1.497) = 0.068

The null hypothesis is failed to be rejected. There is not enough evidence to support the claim that the mean SAT-M score of all Ross College students is higher than the national mean .

For more information, refer to the link given below:

https://brainly.com/question/20165896