Question

One way to evaluate the effectiveness of a course instructor is to examine the scores achieved by his or her students in an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information - some teachers have a style that works very well with more able students but is unsuccessful with less able or poorly motivated students. A professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300. A new instructor has a class of thirty students, whose test scores had a sample quasi-variance of 480. Regarding these students’ test scores as a random sample from a normal population:

(a) At a 5% significance level, test against a two-sided alternative the null hypothesis that the population variance of their scores is 300.

(b) Based on your answer to 4a, decide if a 95% confidence interval for the population variance would include the value of 300.

(c) Calculate the power of the test.

(d) Draw the power function from 4c in R.

(e) Looking at the graph from 4d, what is the probability of Type II error for σ 2 = 500 (roughly)?

Answer 1

a)

n = 30 , s^2 = 480

b)

since we reject the null hypothesis at 5% level, 300 should not be present in confidence interval

We can calculate the CI also to confirm the same,

300 is not present in confidence interval

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