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aliya0001 [1]
3 years ago
15

A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test thi

s claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000.The following is the setup for this hypothesis test:{H0:p=0.40Ha:p<0.40Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Mathematics
1 answer:
bearhunter [10]3 years ago
4 0

Answer:

The statistic for this case would be:

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

And replacing we got:

z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92

Step-by-step explanation:

For this case we have the following info:

n =700 represent the sample size

X= 305 represent the number of employees that earn more than 50000

\hat p=\frac{305}{700}= 0.436

We want to test the following hypothesis:

Nul hyp. p \leq 0.4

Alternative hyp : p>0.4

The statistic for this case would be:

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

And replacing we got:

z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92

And the p value would be given by:

p_v = P(z>1.922)= 0.0274

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