Question

A certain index tracks daily how people from a certain country evaluate their lives, both now and in five years, on a certain striving scale, where "0" represents the worst possible life and "10" represents the best possible life. Respondents are classified as "thriving" if they rate their current life a 7 or higher and their future life an 8 or higher. Daily results are based on a three-day rolling average, based on telephone interviews with 981 adults from that country. A recent report stated that 588 of 981 adults were thriving. Do these responses provide strong evidence that more than 55% of adults are thriving? Correct the mistakes you find in the following student's attempt to test an appropriate hypothesis.

Are the hypotheses correct?

A. The hypotheses are correct.

B. No because the hypotheses should be H0: p=0.55 vs. HA:p>0.55.

C. No because the hypotheses should be H0: p=0.55 vs. HA: p≠0.55.

D. No because the hypotheses should be H0: p=0.55 vs. HA: p≠0.55.

Did the student address all of the conditions correctly?

A. Yes. The conditions are correct.

B. No because the sample is not a simple random sample.

C. No because the correct conditions are SRS, 981<10% of all adults, the number of successes is 588, and the number of failures is 393.

D. No because the correct conditions are SRS, np=981(0.55)=539.55, and nq=981(0.45)=441.45.

Are the calculations for the confidence interval correct? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. The calculations for the confidence interval are correct.

B. The calculations for the confidence interval are not correct because SEp should be used instead of SDp. The correct confidence interval is. (Round to three decimal places.)

C. The calculations for the confidence interval are not correct because z*=1.645. The correct confidence interval is

(Round to three decimal places.)

D. The calculations for the confidence interval are not correct because p is incorrect. The correct confidence interval is (Round to three decimal places.)

Is the interpretation correct?

A. The interpretation is correct.

B. The interpretation is not correct. Since 0.55 is not within the interval, the true percentage of those who are "thriving" is not 55%.

C. The interpretation is not correct because the proportion of days when people are thriving is 0.599.

D. The interpretation is not correct. Since 0.55 is within the interval, it's a plausible value for the true proportion of those who are "thriving."

Answer #1

Given, X = 588 and n = 981

P = X/n = 588/981 = 0.5994

Hypothesis:

H0: p=0.55 vs. HA:p>0.55.

Conditions:

np=981(0.55)=539.55, and nq=981(0.45)=441.45

np and nq > 10

conditions are met

90% Confidence interval:

Zc = 1.645 (Use Z table)

CI = P +/- Zc*SEp

SEp = SQRT(P(1-P)/n) = SQRT(0.5994*(1-0.5994)/981) = 0.0156

CI = 0.5994 +/- 1.645*0.0156

CI = (0.5737, 0.6251)

The above confidence interval does not include null value 0.55, so, we reject H0

Therefore, there is enough evidence to claim that more than 55% of adults are thriving

Note: Please follow the steps

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