Question

1)At a certain university, the average cost of books was $370 per student last semester and the population standard deviation was $75. This semester a sample of 55 students revealed an average cost of books of $400 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?

a)0.40

b)0.55

c)22.00

d)2.97

2)It has been claimed that at UCLA at least 40% of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at  = .01?

a)No because the test value is in the rejection region

b)Yes because the test value is not in the rejection region

c)Yes because the test value is in the rejection region

d)No because the test value is not in the rejection region

Answer 1

1)

The test hypothesis is


This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side
Now, the value of test static can be found out by following formula:

OPTION D: 2.97

2)
Proportion = 0.4
Total number of sample (n) = 250
number of favourable events (X) = 90


We are interested in testing the hypothesis




Since, the test is two-tail test at


Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -2.3263478740408408 or greater than the critical value 2.3263478740408408

The statistic value, -1.291 is greater than the critical values -2.3263478740408408 . Therefore, we fail to reject the null hypothesis.

OPTION B) Yes, because the test value is not in the rejection region.

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