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 of100 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 quantitative 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 classified based on the characteristic of being satisfied or not.

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

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 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 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 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 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 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.

Since the sample size is no

more

less

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

skewed right

uniform

with mu Subscript ModifyingAbove p with caret Baseline equalsμp=(BLANK)

and

sigma Subscript ModifyingAbove p with caret Baseline equalsσp=(BLANK).

​(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

0.7878​?

The probability that proportion who are satisfied with the way things are going in their life exceeds 0.7878 is BLANK

​(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 BLANK, which

▼

is not

is

unusual because this probability

▼

is

is not

less than

▼

5

0.05

0.5

50

​%.

​(Round to four decimal places as​ needed.)

Answer 1

a)

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

b)

option 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)

Since the sample size is no more than​ 5% of the population size and np(1−p)equals=(100*0.76*0.24=)18.24 greater than or equals≥​10, the distribution of p hat is approximately normal with =0.76 and =((0.76*0.24/100) = 0.043

d)

The probability that proportion who are satisfied with the way things are going in their life exceeds 0.78

P(X>0.78) =

Z=(0.78-0.76)/0.043 = 0.4651

P(X>0.78) =P(Z≥0.4651)= 1 - 0.6791 = 0.3209

e)here p cap=70/100 =0.70

The probability that 70 or fewer people in the sample are satisfied is 0.0815, which

is not unusual because this probability is not less than 5%