Question Help According to a study conducted by a statistical organization, the

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Question Help 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 0.86. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below (a) Suppose the random sample of 100 people is asked. "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain. O A. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not. B. The response is quantitative because he responses can be measured numerical and he values added or subtracted providing meaning u results. O C. Theresponse is qualitative because the responses can be classified based on the characteristic of being satisfied or not. O D. The response is qualitative because the responses can be measured numerically and the values added or subtracted, providing meaningful results. (b) Explain why the sample proportion. p. is a random variable. What is the source of the variability? O A. The sample proportion P is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. OB. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that diferent people feel differently regarding their satisfaction OC. The sample proportion p is a random variable because the value of 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. OD. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully (c) Describe the sampling distribution of 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 no than 5% of the population size and np I--210 the distribution of p is Click to select your answers). | with ^ = | | and ^-

Explanation / Answer

Part (a)

Response would be ‘yes’ or ‘no’. This is qualitative, rather categorical to be more precise.

So, Option (c) ANSWER

Part (b)

The perception and level of satisfaction differ from person to person. Since pcap is based on a random sample of persons whose perception and level of satisfaction differ from person to person, pcap is a variable. But, it would exhibit a probabilistic pattern and hence it is random.

So, Option (a) ANSWER

Part (c)

Proportion, in general, is Binomially distributed. But, when the sample size is at least 5% and np(1 - p) 10, the distribution of pcap can be taken as Normal with mean = p and standard deviation = sqrt{p(1- p)/n}

We have, n = 100, p = 0.86, 1 – p = 0.14. So, np(1 - p) = 12.04 10; p(1 - p) = 0.1204; sqrt{p(1- p)/n} = sqrt(0.001204) = 0.0347.

Thus, answers to be selected to fill in the blanks are, in the given order: ‘less’, ’12.04’, ‘Normal’, ‘0.86’ and ‘0.0347’ ANSWER

Part (d)

As seen in Part (c), pcap ~ N(0.86, 0.0347) and hence, Z = {(pcap – 0.86)/0.0347} ~ N(0, 1).

Now, w want P(pcap > 0.88) = P(Z > 0.5764) = 1 – 0.7178 = 0.2822 [obtained using Excel]

So, ANSWER is 0.2822.

Part (e)

Here we must evaluate P(pcap 0.8) [80 out of 100 responding ‘satisfied’ implies pcap 0.8] = P(Z - 1.7292) = 0.0519 [obtained using Excel]

Normally, a probability less than 5% (0.05) is considered unusual.

So, answers to be selected to fill in the blanks are, in the given order: ‘0.0519’, ‘is not’, ‘is not’ and ‘5’. ANSWER

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