Question

A school social worker is interested in testing the claim that less than 89% of teenagers graduate from high school. To test this claim, the school social worker collects the following data on a sample of 380 teenagers and 320 of them graduated from high school. The following is the data from this study:

Sample size 380 teenagers
The alternative hypothesis is H: p< 0.89
The test statistic is calculated as zo =-2.98.

Find and interpret the p- value for this hypothesis test.

Answer 1

z= -2.93

|z| = |-2.93|=2.93there fore we accepted Alternative hypothesis

The calculated z =2.93 > 1.6 the tabulated value at 89% level of significance.

A school social worker is interested in testing the claim that less than 89% of teenagers graduate from high school.

Explanation:

Step(i)

Given sample of 380 teenagers and 320 of them graduated from high school

The proportion of sample is
`p = (320)/(380) = 0.842`

Given a school social worker is interested in testing the claim that less than 89% of teenagers graduate from high school

The population proportion 'P' = 0.89

Null hypothesis:- H₀: p= 0.89

Alternative hypothesis: H: p< 0.89

Step(ii)

The test statistic

`Z = \frac{p-P}{\sqrt{(PQ)/(n) } }`

`Z = \frac{0.84210-0.89}{\sqrt{(o.89X0.11)/(380) } }`

on calculation , we get

`z = (-0.047894)/(0.016049)`

z = -2.93

|z| = |-2.93|=2.93

we will use 89% of level of z- score =1.6 (check normal diagram)

The calculated z =2.93 > 1.6 the tabulated value at 89% level of significance.

we rejected null hypothesis

we accepted alternative hypothesis

Conclusion:-

A school social worker is interested in testing the claim that less than 89% of teenagers graduate from high school.