Question

The mean SAT score in mathematics is 554. The standard deviation of these scores is 39. A special preparation course claims that the mean SAT score, HI, of its graduates is greater than 554. An independent researcher tests this by taking a random sample of 60 students who completed the course; the mean SAT score in mathematics for the sample was 567. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 5542 Assume that the population standard deviation of the scores of course graduates is also 39. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. μ a р H.: 0 H: 0 х S ê 0. DO (b) Determine the type of test statistic to use. (Choose one) ロ=口 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) O . $ ?
(d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 554? Yes No

Answer 1

We have the following details

mean = 554

n = 60

bar x = 567

alpha = 0.01

How to solve for the hypothesis

A. h0. u = 554

H1. u > 554

B. Given that the standard deviation is known what we have to make use of is the independent z test

test statistics calculation

567-554/(39/√60)

= 2.582

d. at alpha = 0.01 and test statistics = 2.582, the value of the p value = 0.0049

0.0049  < 0.01. So we have to reject the null hypothesis.

e. Yes We have to accept that  we support the preparation course's claim that the population mean SAT score of its graduates is greater than 554

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