Question

Sunshine High School claims that 72% of its students complete their homework on a daily basis. Ms. Carter surveyed 80 students and found that only 60% complete their daily homework. What does the test statistic calculation look like in this situation for an appropriate hypothesis test? z equals 0.60 minus 0.72 all over the square root of the quantity 0.72 times 0.28 over 80 z equals 0.60 minus 0.72 all over the square root of the quantity 0.60 times 0.40 over 80 z equals 0.60 minus 0.72 all over the square root of the quantity 0.60 times 0.72 over 80 z equals 0.72 minus 0.60 all over the square root of the quantity 0.60 times 0.40 over 80 z equals 0.72 minus 0.60 all over the square root of the quantity 0.72 times 0.28 over 80

Answer 1

Option A)

z equals 0.60 minus 0.72 all over the square root of the quantity 0.72 times 0.28 over 80

Explanation:

We are given the following in the question:

Sample size, n = 80

p = 72% = 0.72

`\hat{p} = 60\5 = 0.60`

Formula for z-statistic:

`z = \frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

Putting the values, we get,

`z = \displaystyle\frac{0.60-0.72}{\sqrt{(0.72(1-0.72))/(80)}}\\\\z =\displaystyle\frac{0.60-0.72}{\sqrt{(0.72(0.28))/(80)}} = -2.39`

This, the correct answer is

Option A)

z equals 0.60 minus 0.72 all over the square root of the quantity 0.72 times 0.28 over 80