MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
d, e
According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.82. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. (a) Choose the appropriate statement about the sample proportion \( \hat{p} \): - A. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. - B. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. - C. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. - D. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. (c) Describe the sampling distribution of \( \hat{p} \), the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is \(\_\_\_\_\_) (dropdown) than 5% of the population size and \( np(1 - p) \geq 10 \), the distribution of \( \hat{p} \) is (dropdown) with \( \mu_{\hat{p}} = \_\_\_ \) and \( \sigma_{\hat{p}} = \_\_\_\). (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.84? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.84 is \_\_\_. (Round to four decimal places as needed.) (e
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Transcribed Image Text:According to a study conducted by a statistical organization, the proportion of people who are satisfied with the way things are going in their lives is 0.82. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. (a) Choose the appropriate statement about the sample proportion \( \hat{p} \): - A. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. - B. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. - C. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. - D. The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. (c) Describe the sampling distribution of \( \hat{p} \), the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is \(\_\_\_\_\_) (dropdown) than 5% of the population size and \( np(1 - p) \geq 10 \), the distribution of \( \hat{p} \) is (dropdown) with \( \mu_{\hat{p}} = \_\_\_ \) and \( \sigma_{\hat{p}} = \_\_\_\). (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.84? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.84 is \_\_\_. (Round to four decimal places as needed.) (e
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