Question

PLS HELP: I am unsure how to calculate this into final numbers.

Cal Amity decided to survey 880 inhabitants of the Kingdom so that he could have a confidence level of 95% and a margin of error of 3%. He found that 72% of his sample answered "yes" to the second survey question, which was, "Have you done anything, or will you do anything, to prepare your kitchen for Gourmando's visit?"


Mr. Amity can infer that, most likely, between _[blank A]_ and _[blank B]_ inhabitants of the Kingdom have done, or will do something, to prepare their kitchen before Gourmando's visit.

Options:

blank A: 3450

blank B: 5000

blank A: 0

blank B: 300

blank A: 3600

blank A: 150

blank B: 3600

blank B: 3750

Answer 1

Complete question :

Cal Amity decided to survey 880 inhabitants of the Kingdom so that he could have a confidence level of 95% and a margin of error of 3%. He found that 72% of his sample answered "yes" to the second survey question, which was, "Have you done anything, or will you do anything, to prepare your kitchen for Gourmando's visit?"

Mr. Amity can infer that, most likely, between _[blank A]_ and _[blank B]_ inhabitants of the Kingdom have done, or will do something, to prepare their kitchen before Gourmando's visit.

If a population is 5000

Answer:

blank A: 3450

blank B: 3750

Explanation:

Number of inhabitants surveyed = 880

Population size = 5000

Error margin = 3%

Percentage that answered 'yes' = 72%

The confidence interval :

Mean ± Error margin

Lower Bound = 72% - 3% = 69% = 0.69

Upper bound = 72% + 3% = 75% = 0.75

Since the question want us know the overall inhabitants of the kingdom who fall between this interval :

Blank A = lower boundary = 0.69 * 5000 = 3450

Blank B = upper boundary = 0.75 * 5000 = 3750