Question

In: Statistics and Probability

According to a study conducted by a statistical​ organization, the proportion of people who are satisfied...

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).

Solutions

Expert Solution


Related Solutions

According to a study conducted by a statistical​ organization, the proportion of people who are satisfied...
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. A. The response is...
According to a study conducted by a statistical organization, the proportion of Americans who are satisfied...
According to a study conducted by a statistical organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.66. Suppose that a random sample of 205 Americans is obtained, a. About 69% of the samples will contain more than x Americans who are satisfied with their lives. Find the x. b. What is the probability that at least 140 Americans in the sample are satisfied with their lives? c. What is the...
According to a study conducted by a statistical​ organization, the proportion of Americans who are satisfied...
According to a study conducted by a statistical​ organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.76. Suppose that a random sample of 110 Americans is obtained. Complete parts​ (a) through​ (c). (a) Describe the sampling distribution of p. (b) Using the distribution from part​ (a), what is the probability that at least 80 Americans in the sample are satisfied with their​ lives? (c) Using the distribution from part​ (a),...
12-According to a study conducted by a statistical organization, the proportion of Americans who are satisfied...
12-According to a study conducted by a statistical organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.66. Suppose that a random sample of 205 Americans is obtained, -About 69% of the samples will contain more than x Americans who are satisfied with their lives. Find the x. -What is the probability that at least 140 Americans in the sample are satisfied with their lives? -What is the probability that 157...
According to a study, the proportion of people who are satisfied with the way things are...
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...
1.The Government is interested in the proportion of people who are either Satisfied or Very Satisfied...
1.The Government is interested in the proportion of people who are either Satisfied or Very Satisfied with current Government Change policies. They believe that they have the support of the majority of American. You are to conduct a hypothesis test to check their Claim. The random sample of 400 customers shows that 225 people were either Satisfied or Very Satisfied with the current Government policies. Write down the Null and Alternative hypotheses in both Symbols and Words for the above...
4. A study was conducted to determine the proportion of people who dream in black and...
4. A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 322 people over the age of​ 55, 75 dream in black and​ white, and among 281 people under the age of​ 25, 19 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25....
1) A study was conducted to determine the proportion of people who dream in black and...
1) A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 323 people over the age of​ 55, 66 dream in black and​ white, and among 281people under the age of​ 25,15 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts​...
A study was conducted to determine the proportion of people who dream in black and white...
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 309 people over the age of​ 55, 63 dream in black and​ white, and among 315 people under the age of​ 25,13 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts​...
A study was conducted to determine the proportion of people who dream in black and white...
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 298 people over the age of​ 55, 61 dream in black and​ white, and among 290 people under the age of​ 25, 14 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Find...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT