Question

The Survey of Study Habits and Attitudes (SSHA) is a phychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives that the SSHA to 25 students who are at least 30 years of age. Their mean is ¯x = 127.8.

(a) Assuming that σ = 30 for the population of older students, carry out a test of

H0 : µ = 115

Ha : µ > 115

Report the P-value of your test, and state your conclusion clearly.

(b) Your test in part (a) required two important assumptions in addition to the assumption that the value of σ is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?

Answer 1

mean score for U.S. college students = = 115

standard deviation = = 30

Here sample mean = = 127.8

(a) Here population of standard deviation is given that is 30.

H₀ : µ = 115

H_a : µ > 115

sample size = n = 25

standard error of sample mean = /sqrt(n) = 30/sqrt(25) = 6

Test statistic

Z = (127.8 - 115)/6 = 2.1333

P - value = P(Z > 2.1333) =1 - P(Z < 2.1333) = 1 - 0.9836 = 0.0144

so here we say that we would reject the null hypothesis and sayt hat mean score is higher than 115 marks.

(b) Here the assumptions are

(i) Interval or ratio scale of measurement (approximately interval)

(ii) Random sampling from a defined population that is approximately normally distributed.

(iii) The  value of σ is known.

Here the assumption of random sampling is most important.