1 The union representing a group of office workers tasked wi

1. The union representing a group of office workers tasked with data entry at a computer terminal claims that the working conditions have caused chronic pain in at least 25 percent of workers. The employer, trying to show that the claim is not true, carries out a study involving 87 workers. It showed that 17 of them did indeed experience chronic pain that was due to the working conditions.

What is the sample value of the test statistic?

-1.729

-1.176

1.176

1.960

2. Continuing with the previous question, would we reject the Union\'s claim (the null hypothesis) at a significance level of 0.05?

Yes, because the sample value is a negative number.

Yes, because the p-value of 0.042 is less than 0.05

No, because the p-value of 0.1198 is more than 0.05

No, because the p-value is a negative number which is impossible.

3. Suppose that someone claims that hte median salary fo rindividuals in New Jersey with a business degeree is at $85,000 or more. you feel that this is too high, so you collect a sample of 160 such individuals and find that 95 of them earn less than $85,000 and the other 65 earn more than that.

Using a significance level of 0.05, what is/are the critical value(s) for this hypthesis test.

-1.96 and +1.96

-1.64 and +1.64

-1.64

+1.64

4. Contiuing with the previous question (about NJ individuals with business degrees,) what is the sample value of the test statistic?

-2.29

-1.64

0.37

4.03

5. Using the information from the previous two questions, would we reject the individual\'s claim?

We do not know the size of the sample, so it is not possible to answer this question.

No, becuase the p-value is greater than 0.05.

Yes, because the p-value is greater than 0.05

Yes, because the sample value falls into the rejection region.

Solution

1.
          
Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >   0.25
Ha:   p   <=   0.25
As we see, the hypothesized po =   0.25      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.195402299      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[p^(1 - p^)/n] =    0.046423835      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.176 [ANSWER, 2ND OPTION]

2.

To reject HA of a right tailed test, z has to be positive. Thus, the answer is

OPTION 1: Yes, because the sample value is a negative number. [ANSWER]

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