Samples of students taking an introduction to statistics course at a four-year c

Question

Samples of students taking an introduction to statistics course at a four-year college and at a community college were asked their age with the results summarized below a. Test at the 0.05 level of significance to determine if students taking an introduction to statistics course at the community college are older on average than students taking an introduction to statistics course at the four-year college. Use degrees of freedom of 31. (df =31). b. Determine a 90% confidence interval for the difference in average age of students taking an introduction to statistics course the community college and at the four-year college. Use degrees of freedom of 31. (df =31).

Explanation / Answer

Null hypothesis: 1 - 2 <= 0
Alternative hypothesis: 1 - 2 > 0

a) x1 = 20.7 , x2 = 22.3 , n 1 = 50 , n2 = 32 , s1 = 2.7 , s2 = 4.4

SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(2.7^2/50) + (4.4^2/32)]
= 0.866

t = [ (x1 - x2) - d ] / SE
= [(20.7 - 22.3) - 0] / 0.866
= -1.846

p value is calculated using t = -1.846 , df = 31
P value = 0.0372

we reject the null hypothesis

b) z value at 90% CI = 1.645

CI = ( x1 - x2 ) +/- z * sqrt[(s1^2/n1) + (s2^2/n2)]
= (20.7 - 22.3) +/- 1.645 * sqrt[(2.7^2/50) + (4.4^2/32)]
= (-3.0253 , -0.1746)

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