Question

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?

Answer 1

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)