across some data about the population at large. From the Bureau of Labor Statist
ID: 3360405 • Letter: A
Question
across some data about the population at large. From the Bureau of Labor Statistics, they found that in the U.S. population, the average monthly salary for accountants is $2400, with a standard deviation of $275. The average salary of accountants at the firm they sampled, GOB Enterprises, (n=169) is $2000 per month. Should Sandra move across the country to join GOB or keep looking?
Sandra is trying to determine if the average salary at GOB is less than the population. State their null and research hypothesis using symbols and words. 5 Points.
Using the information presented above, calculate the z-statistic and its associated p-value. Round the z-score to two decimal points and report all four digits of the p-value. 5 Points.
Sandra needs to find the critical region to test his hypothesis and decides to set the alpha level of 0.05. Report the z-critical value(s) that mark off the rejection zone for this test. HINT: Use Appendix A to help construct your critical region. Be specific about whether your z-critical value is positive, negative, or both. 5 Points.
Using the information calculated in steps 1 – 4, decide whether Sandra can reject the null hypothesis. On your own paper, draw the curve and shade the region(s) to help you figure it out. In 3 – 5 sentences, explain why they can, or cannot, reject the null hypothesis and what this indicates about their job decision. 5 Points.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 2400
Alternative hypothesis: < 2400
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.
Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 21.154
z = (x - ) / SE
z = - 18.91
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a z statistic test statistic of - 18.91.
Thus the P-value in this analysis is less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the average salary at GOB is less than the population.
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