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

Answer 1

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

Step-by-step explanation:

let p be the population proportion of students complete their homework on a daily basis.

As per given , we have

p= 0.72

sample size : n= 80

Sample proportion : $\hat{p}=0.60$

Test statistic for proportion:

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

i.e.

$z=\dfrac{0.60-0.72}{\sqrt{\dfrac{0.72(1-0.72)}{80}}}$

i.e.

$z=\dfrac{0.60-0.72}{\sqrt{\dfrac{0.72(0.28)}{80}}}$

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