Question

According to a study, 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

100100

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 measured numerically and the values added or subtracted, providing meaningful results.

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 classified based on the characteristic of being satisfied or not.

(b) Explain why the sample proportion, ModifyingAbove p with caretp , is a random variable. What is the source of the variability?

A.The sample proportion ModifyingAbove p with caretp is a random variable because the value of ModifyingAbove p with caretp varies from sample to 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 caretp is a random variable because the value of ModifyingAbove p with caretprepresents 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 ModifyingAbove p with caretp is a random variable because the value of ModifyingAbove p with caretp represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

D.The sample proportion ModifyingAbove p with caretp is a random variable because the value of ModifyingAbove p with caretp 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

ModifyingAbove p with caretp ,

the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.

(c) Describe the sampling distribution of ModifyingAbove p with caretp , 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 less, no more) than 5% of the population size and np(1minus− p)equals=nothinggreater than or equals≥ 10, the distribution of ModifyingAbove p with caretp is ▼(skewed left, approximately normal, uniform, skewed right) with mu Subscript ModifyingAbove p with caret Baseline equalsμp=nothing and sigma Subscript ModifyingAbove p with caret Baseline equalsσp=nothing.

(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 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 68

or fewer people in the sample are satisfied with their lives? The probability that 68 or fewer people in the sample are satisfied is nothing, which ▼(is not, is,) unusual because of this probability( is, is not) less than▼(0.05, 50,0.5,5 )%.

(Round to four decimal places as needed.)

Answer 1

(a)

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

(b)

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

(c)

Here we have

p = 0.76, n=100

The sampling distribution of sample proportion will be approximately normal with mean

p = 0.76 Up

and standard deviation

(1-P) 0.76-0.24 0.0427

Since the sample size is no more than 5% of the population size and np(1minus− p)equals=nothing greater than or equals≥ 10, the distribution of ModifyingAbove p with caretp is approximately normal.

(d)

The z-score for is

p = 0.80

0.80 - 0.76 = 0.94 = 0.0427

The probability that proportion who are satisfied with the way things are going in their life exceeds 0.80 is

P(p > 0.80) = P(z > 0.94) = 1-P(z < 0.94) = 1-0.8264 = 0.1736

(e)

The z-score for is

p = 68/ 100 0.68

0.68 - 0.76 0.04271.8/

The probability that 68 or fewer people in the sample are satisfied is is

P(p < 0.68)-P(z <-1.87) 0.0307