Please show all steps: 1. We will track an SRS of 300 recent GSU math 243 studen

Question

Please show all steps:

1. We will track an SRS of 300 recent GSU math 243 students to see if they eventually take math 244. Assume 15% of all GSU math 243 students eventually take math 244. The exact probablity that p hat will be at least 27% is between:

a. 18.5% and 19% b. 14.5% and 15% c. 8.5% and 9% d. None of these

2. We will track an SRS of 300 recent GSU math 243 students. Assume 15% of all GSU math 243 students eventually take math 244. The count X of students in our SRS that eventually take math 244, has a variance value between:

a. 6 and 6.5 b. 38 and 38.5 c. 0.02 and 0.025 d. None of these

Explanation / Answer

a) = sqrt[ P * ( 1 - P ) / n ], P is the hypothesized value of population proportion in the null hypothesis, P = 0.15
= sqrt[0.15*(1-0.15)/300] = 0.0206155

z = (p-P)/ = (0.27 - 0.15)/0.0206155 = 5.820855
p-value = 0 , option d. None of these

b) = sqrt[ P * ( 1 - P ) / n ], P is the hypothesized value of population proportion in the null hypothesis, P = 0.15
= sqrt[0.15*(1-0.15)/300] = 0.0206155

Variance of Number of students X = 0.02061552*300 = 38.25

Option b. 38 and 38.5

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