The same STAT 410 instructor believes that only 30% of the students start workin

Question

The same STAT 410 instructor believes that only 30% of the students start working on their homework before Thursday. We wish to test H_0: p lessthaorequalto 0.30 vs H_1: p > 0.30. A random sample of size n = 25 students is obtained a) Find the "best" Rejection Region with the significance level closest to 0.10. (b) What is the power of the Rejection Region obtained in part (a) if p = 0.40? If p = 30.50? c) Suppose that 10 out of 25 students in the sample start working on their homework before Thursday. Find the p-value of the test.

Explanation / Answer

(A)
For 0.1 significance level with 24 degrees of freedom, t-critical value = 1.3178

Critical value of rejection region = 0.3 + 1.3178*sqrt(0.3*0.7/25) = 0.4208

Hence we reject the null hypothesis if the actual value of propotion is greater than 0.4208

(C)

pcap = 10/25 = 0.4

test statistics, t = (0.4 - 0.3)/sqrt(0.3*0.7/25) = 1.09

p-value = 0.14

We reject the null hypothesis as p-value is greater than significance level of 0.1

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