Question

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 0.76 . 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.

A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

B. The response is quantitative because the responses can be measured numerically and the values added or​ subtracted, providing meaningful results.

C. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.

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, ModifyingAbove p with caret ​, is a random variable. What is the source of the​ variability?

A. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret 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.

B. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.

C. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

D. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. ​

(c) Describe the sampling distribution of ModifyingAbove p with caret ​, 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 ▼ more less than​ 5% of the population size and ​np(1minus ​p)equalsnothinggreater than or equals​10, the distribution of ModifyingAbove p with caret is ▼ skewed right uniform skewed left approximately normal with mu Subscript ModifyingAbove p with caret Baseline equals nothing and sigma Subscript ModifyingAbove p with caret Baseline equals nothing . ​(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 0.80 ​? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.80 is nothing . ​(Round to four decimal places as​ needed.)

​(e) Using the distribution from part​ (c), would it be unusual for a survey of 100 people to reveal that 70 or fewer people in the sample are satisfied with their​ lives? The probability that 70 or fewer people in the sample are satisfied is nothing ​, which ▼ (is) or (is not) unusual because this probability ▼ (is not) or (is) less than ▼ (0.05) or (0.5) or (50) or (5) ​%. ​(Round to four decimal places as​ needed.) Click to select your answer(s).

Answer 1