A random sample of 90 eighth grade students\' scores on a national mathematics a

Question

A random sample of 90 eighth grade students' scores on a national mathematics assessment test has a mean score of 286 with a standard deviation of 32. This test result is more than 280. At alpha = 0.06, is there enough evidence to support the administrators claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H_0 and H_a. Choose the correct answer below. A. H_0: mu greaterthanorequalto 280 (claim) H_a: mu 280 (claim) C. H_0: mu = 280 (claim) H_a: mu > 280 D. H_0: mu lessthanorequalto 280 H_a: mu > 280 (claim) (b) Find the standardized test statistic z, and its corresponding area. z = (Round to two decimal places as needed.) Area = (Round to three decimal places as needed.)

Explanation / Answer

(a) H0 : <= 280

H1 : > 280 (claim)

Option D is correct.

(b) Test Statistic

z = (xbar - H)/ (s/n) = (286-280)/ (32/90) = 6/ 3.3731 = 1.78

Area = Pr( x >=286; 280; 3.373) = 1- 0.9725 = 0.028

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