Statistics and Probability

Question

Given below are the number of successes and sample size for a simple random sample from a population.

x = 12​, n = 40​, 90​% level

a. Determine the sample proportion.

b. Decide whether using the​ one-proportion z-interval procedure is appropriate.

c. If​ appropriate, use the​ one-proportion z-interval procedure to find the confidence interval at the specified confidence level.

d. If​ appropriate, find the margin of error for the estimate of p and express the confidence interval in terms of the sample proportion and the margin of error.

Answer 1

The sample proportion (phat) is 12/40 = 0.3

Since the number of successes (12) and failures (28) is greater than 10, the one-proportion z interval procedure is appropriate.

CI = phat +/- z-critical * sqrt(phat* (1-phat)/n) = 0.3 +/- 1.645 * sqrt(0.3*0.7/40) = 0.3 +/- 0.119.

The margin of error is 0.119.

CI is 0.181,0.419. Expressed in terms of margin of error is 0.3 +/- 0.119.

Answer 2

My solution is found in this link:

https://drive.google.com/file/d/1D_13yNzf_TgffUgbmXbu7IgeALGLH0I7/view?usp=sharing

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