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The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation σ = 20. You suspect that incoming freshman have a mean μ, which is different from 110 because they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses

H0: μ = 110, Ha: μ 110


You give the SSHA to 50 students who are incoming freshman and find their mean score.


Suppose you observed the same sample mean = 115.35, but based on a sample of 100 students. What would the corresponding P-value be?

Verified Answer :

ghostfire14

Dang...H0: μ = 115
HA: μ ≠ 115
Sample mean = 120
Standard deviation = 25
Standard error of mean = σ / √ n
Standard error of mean = 25 / √ 100
SE = 25/10
Standard error of mean 2.5
z = (xbar- μ ) / SE
z = (120-115) / 2.5
z = 2
p-value = 2 P( z > 2) = 2(0.0228) = 0.0456
the data are statistically significant at level = .05, but not at level = .01.

2)
H0: μ = 115
HA: μ ≠ 115
Sample mean = 119
Standard deviation = 25
Standard error of mean = σ / √ n
Standard error of mean = 25 / √ 100
SE = 25/10
Standard error of mean 2.5
z = (xbar- μ ) / SE
z = (119-115) / 2.5
z = 1.6
p-value = 2P( z > 1.6) = 2(0.0548) =0.1096

3)
a statement about the population the researcher suspects is true, and is trying to find evidence for.

4)
Sample mean = 80
Standard deviation = 20
Standard error of mean = σ / √ n
Standard error of mean = 20 / √ 100
SE = 20/10
The Standard error of mean 2
Confidence interval 80-(2)(1.645)
and 80+(2)(1.645)
(76.7, 83.3)

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