Question

# A certain index tracks daily how people from a certain country evaluate their​ lives, both now...

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."

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