Question

A certain bank performed a study in 2012 of 1050 residents from a certain country 18 years of age and older. It was reported that 68​% of residents have a certain retirement savings plan. A study from 2000 reported that 57​% of residents had the same retirement savings plan. Complete parts a and b below. ​a) Create a 95​% confidence interval for the proportion of adults in the country who have invested in a retirement savings account based on the survey in 2012. The confidence interval is left parenthesis nothing comma nothing right parenthesis . ​(Type integers or decimals rounded to three decimal places as​ needed.) ​b) Does this provide evidence of a change from 2000 in retirement savings investing among adults in the​ country? Using your confidence​ interval, test an appropriate hypothesis and state your conclusion. Determine the hypotheses for this test. Choose the correct answer below. A. Upper H 0​: pequals0.68 Upper H Subscript Upper A​: pgreater than0.68 B. Upper H 0​: pequals0.57 Upper H Subscript Upper A​: pgreater than0.57 C. Upper H 0​: pequals0.57 Upper H Subscript Upper A​: pless than0.57 D. Upper H 0​: pequals0.68 Upper H Subscript Upper A​: pnot equals0.68 E. Upper H 0​: pequals0.57 Upper H Subscript Upper A​: pnot equals0.57 F. Upper H 0​: pequals0.68 Upper H Subscript Upper A​: pless than0.68 What does the confidence interval​ indicate? Explain. Since the percentage of adults who had the retirement savings plan ▼ is is not in the confidence​ interval, ▼ fail to reject reject Upper H 0. ​So, there ▼ is is not strong evidence that the true proportion in 2012 is the same as it was in 2000. The study in 2012 indicates the percentage of adults who have a retirement savings account ▼ increased. stayed the same. decreased.

Answer 1

(a)

0.652	confidence interval 95.% lower
0.708	confidence interval 95.% upper

(b) The hypothesis being tested is:

H0: p = 0.57

Ha: p ≠ 0.57

Since the percentage of adults who had the retirement savings plan is not in the confidence​ interval, reject H0. ​So, there is not strong evidence that the true proportion in 2012 is the same as it was in 2000. The study in 2012 indicates the percentage of adults who have a retirement savings account increased.