A science assessment test was administered on two randomly selected of female an

Question

A science assessment test was administered on two randomly selected of female and male high school students. The results of the test are summarized below: Male n_1 = 49 x_1 = 300.4 s_1 = 1.6 Female n_2 = 50 x_2 = 299.6 s_2 = 1.5 At alpha = 0.05, do the data provide sufficient evidence to conclude that mean score for the male students was higher than that of the female students? a) State the null and the alternative hypotheses of the claim. H_0: H_a: b) Find the value of the standardized test statistic. c) Find the p-value for the test. d) At alpha = 0.05, state your decision and interpret it in the context of the problem.

Explanation / Answer

a)

Ho : mu1 - mu2 = 0

Ha; mu1 -mu2 > 0

b)

n1 = 49 , n2 = 50 , x1 = 300.4 , x2 = 299.6 , s1 = 1.6 , s2 = 1.5

SE = sqrt [(s12/n1) + (s22/n2)]
SE = sqrt[(1.6^2/49) + (1.5^2/50]

= 0.312

t = [ (x1 - x2) - d ] / SE

= [ (300.4 - 299.6) - 0 ] / 0.312

= 2.56

c ) P value is calculated using t = 2.56 with df = 97

P value = .006005.

d) As p value is less than 0.05 . So, we reject the null hypothesis.

There is sufficient evidence to conclude that the mean score for male students was higherthan that of female students

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