Question

7. According to a study conducted by a statistical organiza tion, the proportion of people who are satisfied with the way thie are going in their lives is 0.80. 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 satisfed with the way things are going in your lifte7" ls the response to this question quaitative or quantitative? Explairn O A. The response is quantitative because the responses can be classified based on the O B. The response is qualitative because the responses can be measured numerically and the O C. The response is quantitative because the responses can be measured numercaly and the OD. The response is qualitative because the responses can be classfied based on the (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 represents a random characteristic of being satisfed or not values added or subtracted, providing meaningful results values added or subtracted, providing meaningful results characteristic of being satisfied or not person included in the sample. The variablity is due to the fact that dfferent people feel differently regarding their satsfaction. O B. The sample proportion p is a random variable because the value of p represents a random due to the fact that people may not be person included the sample The variabilty responding to the question truthfully O C. 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 dfferently regarding their O. 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 venty the model requirements Since the sample size is no (1) -than 5% of the population size and npl 1-p) 2 10, the and ơ.. distribution of p is (2)_ 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) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 74 or fewer people in the sample are satisfied with their lives? The probability that 74 or fewer people in the sample are satisfied is which (3)unusual less than (5) because this probability (4) (Round to four decimal places as needed)

Answer 1

(a) Option (d)

(b) Option (c)

(c) Since the sample size no more than 10% of the population size and np(1 - p) ≥ 10, the distribution of p^ is a normal distribution with μp = np = 100 * 0.8 = 80.000 and σp = √(np(1 - p)) = √(100 * 0.8 * (1 - 0.8)) = 4.000

(d) np' = 100 * 0.84 = 84

z = (84 - 80)/4 = 1

P(p' > 0.84) = P(z > 1) = 0.1587

(e) z = (74 - 80)/4 = -1.5

P(x ≤ 74) = P(z < -1.5) = 0.0668

This is not unusual since the probability is not less than 5%.