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.

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