Question

"A random sample of 50 university admissions officers was asked about expectations in application interviews. Of these sample members, 28 agreed that the interviewer usually expects the interviewee to have volunteer experience doing community projects. Test the null hypothesis that on-half of all interviewers have this expectation against the alternative that the population proportion is larger than one-half. Use α= 0.05."

Answer 1

Explanation:

given that a random sample of 50 university admissions officers was asked about expectations in application interviews.

Sample proportion =
`(28)/(50) =0.56`

`H_0: p = 0.5\\H_a: p >0.5\\`

(Right tailed test at 5% significance level)

p difference = 0.06

Assuming H0 to be true p will have normal distribution with

std error =
`\sqrt{(0.5*0.5)/(50) } \\=0.0707`

Test statistic = p difference/std error

=
`(0.06)/(0.0707) \\=0.8485`

p value = 0.19808

Since p is greater than alpha, we accept null hypothesis

There is statistical evidence to support that the sample proporiton is only 0.50

Answer 2

There is statistical evidence to support that the sample proportion is only 0.50.

Explanation:

given that a random sample of 50 university admissions officers was asked about expectations in application interviews.

Sample proportion =
`(28)/(50)`

`H_0:p=5`

`H_0:p>5`

(Right tailed test at 5% significance level)

p difference = 0.06

Assuming H0 to be true p will have normal distribution with

std error =
`\sqrt{(0.5*0.5)/(50) }`

Test statistic = p difference/std error

=
`(0.06)/(0.0707)`

=0.8485

p value = 0.19808

Since p is greater than alpha, we accept null hypothesis

There is statistical evidence to support that the sample proportion is only 0.50.