Question

# a survey measures the motivation, attitudes, and study habits of freshman in college. freshmans’ scores on...

a survey measures the motivation, attitudes, and study habits of freshman in college. freshmans’ scores on this survey range from 0 to 200 and follow (approximately) a normal distribution, with mean of 110 and standard deviation σ = 20. you suspect that the next group of freshman will have a mean μ, which is different from 110 because they are often excited yet anxious about leaving college. to verify your suspicion, you test the hypotheses h0: μ = 110, ha: μ ≠ 110 you give the survey to 50 high school seniors who are incoming freshman and find their mean score. suppose you observed the same sample mean of 115.35, but based on a sample of 100 freshman students. what would the corresponding p-value be?

Solution :

= 110

=115.35

= 20

n = 100

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 110

Ha :    110

Test statistic = z

= ( - ) / / n

= (115.35 - 110) / 20/ 100

= 2.675

p(Z > 2.675 ) = 1-P (Z < 2.675 ) = 0.0075

P-value = 0.0075

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