A school administrator wonders if students whose first language is not English s

Question

A school administrator wonders if students whose first language is not English score differently on the math portion of the SAT exam than students whose first language is English. The mean SAT math score of students whose first language is English is 516, on the basis of data obtained from the College Board. SAT math scores are normally distributed with a population standard deviation of 114. Suppose a simple random sample 20 students whose first language was not English results in a sample mean SAT score of 522. The administrator obtains the following output from Minitab and will test his question using a = 0.10.

One-Sample Z

Test of mu = 516 vs not = 516

The assumed standard deviation = 114

N   Mean SE Mean      95% CI         Z      P

20 522.0     25.5 (472.0, 572.0) 0.24 0.814

Are the assumptions for using a hypothesis test satisfied? Explain.

Why did the administrator use a z-test instead of a t-test?

According to the Minitab output, what is the test statistic and what is the p-value?

Should the administrator conclude that the average SAT math score for those whose first language is not English differs from 516? Why or why not

Explanation / Answer

Yes, to perform a z test normality assumption must be made.

Here the null hypothesis is based on one population (sat scores of the students from the school) and the population standard deviation is known. Hence we perform z-test instead of t-test. [ t- test is performed when the standard deviation is not known]

According to the output, the value of the test statistic ie the z value is 0.24 and the p- value is 0.814.

Here, we take a=0.10 ie we want to test the null hypothesis at 10 % level of significance. So we will reject the null hypothesis if p value is less than 0.10 . Here p value is 0.814 > 0.10 . So we fail to reject the null hypothesis. Hence the administrator fails to conclude that the average SAT score for those whose first language is not English differs from 516.

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