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pshichka
1 month ago
5

"A random sample of 50 university admissions officers was asked about expectations in application interviews. Of these sample me

mbers, 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."
Mathematics
2 answers:
PIT_PIT [12.4K]1 month ago
7 0

Answer:

Statistical data suggests that the sample proportion stands at exactly 0.50.

Step-by-step explanation:

This follows from a random sample of 50 university admissions officers surveyed regarding their expectations during application interviews.

Sample proportion = \frac{28}{50}

H_0:p=5

H_0:p>5

(Right tailed test at 5% significance level)

p difference = 0.06

Assuming H0 is valid, p will exhibit a normal distribution with

standard error = \sqrt{\frac{0.5\times0.5}{50} }

Test statistic = p difference/std error

=\frac{0.06}{0.0707}

=0.8485

p value = 0.19808

Given that the p value exceeds alpha, the null hypothesis is accepted

Statistical data suggests that the sample proportion stands at exactly 0.50.

Inessa [12.5K]1 month ago
5 0

Answer:

A study involving 50 university admissions officers surveyed about their expectations during interview applications.

Sample proportion =

(Right-tailed analysis at 5% significance level)\frac{28}{50} =0.56

Difference in p = 0.06

H_0: p = 0.5\\H_a: p >0.5\\Assuming H0 is accurate, p follows a normal distribution with

standard error =

The test statistic is calculated as the difference in p divided by standard error

=

\sqrt{\frac{0.5*0.5}{50} } \\=0.0707

p value obtained = 0.19808

As the p value exceeds alpha, we fail to reject the null hypothesis

\frac{0.06}{0.0707} \\=0.8485Consequently, we do not have statistical grounds to claim that the sample proportion is greater than 0.50

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