The claim that “40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available” is to be investigated at the 0.01 significance level. 74 out of the 200 workers sampled said they would return to work. Let 1-α = 0.99 and α = 0.01. What are the null and alternative hypotheses?

Requirements: 10 questions

Part II. Show your work clearly to receive full credits.

(10 points) Q1. The claim that “40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available” is to be investigated at the 0.01 significance level. 74 out of the 200 workers sampled said they would return to work. Let 1-α = 0.99 and α = 0.01.

What are the null and alternative hypotheses?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value of the test statistic?

What is the calculated (computed) value of the test statistic?

What is the p-value based on the computed test statistic?

State the decision rule and what is your conclusion?

Conduct 99 % confidence interval for population proportion

(15 points) Q2. Kitti wants to study the effectiveness of the Statistics course to improve students’ scores included a pre-testing score and post-testing score of each student. To compare the differences, I computed (post-testing score – pre-testing score). Seven students were randomly selected and completed both tests. The results follow. Let 1-α = 0.99 and α = 0.01.

*Make sure that you set up the hypothesis testing correctly (two-tails, left-tail or right tail)

What are the null and alternative hypotheses?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value of the test statistic?

What is the value of the test statistic to test for differences in the tests?

What is the P-value for differences in the tests?

State the decision rule and your conclusion.

Construct a 99% 2-sided Confidence Interval Estimate for the population difference in the tests.

(15 points) Q3. Kitti wants to investigate the topic of Take-Home Pay. Who earns more money between married or unmarried people? Let 1-α = 0.95 and α = 0.05.

What are the null and alternative hypotheses?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value?

What is the calculated (computed) value of the test statistic?

What is the p-value for the computed test statistic?

State the decision rule and your conclusion.

Construct 95% confidence interval estimate for the difference between married or unmarried people.

(15 points) Q4. Kitti wants to compare the yield of income and growth mutual funds. She wants to investigate whether there a difference in the mean yields of the two funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds, the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal at the 0.05 significance level.

What are the null and alternative hypotheses?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value?

What is the calculated (computed) value of the test statistic? Also, find the pool the sample standard deviations.

What is the p-value for the computed test statistic?

State he decision rule and your conclusion.

Construct 95% confidence interval estimate for the difference between the mean yields of the two funds.

(15 points) Q5. Given the data below, you must show all works and you are not allowed to use only Excel. You can attach an extra page for your calculation works.

What is your research question? Which variable should be X? Which variable should be Y?

Calculate the correlation coefficient (r) and interpret (r)

Calculate the coefficient of determination(r2) and interpret r2

Calculate the regression coefficient of the slope (b)

Calculate the regression coefficient of the Y-intercept (a)

What is the regression equation?

Test for correlation coefficient at the 5% level of significance and make a conclusion

Testing the significance of the slope of the regression line at the 5% level of significance and make a conclusion

What is the standard error of regression?

If number of X increases to 50, what would we predict Y to be?

Answer

(10 points) Q6. The average cost of tuition and room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation (σ) is $1,200. Let 1-α = 0.95 and α = 0.05.

What are the null H0 and alternative hypotheses H1?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value of the test statistic?

What is the calculated (computed) value of the test statistic?

What is the estimated population mean (point estimate)?

What is the margin of error?

Construct 95% confidence interval estimate for the population mean

What is the p-value based on the computed test statistic?

What is your conclusion about the average cost?

(15 points) Q7. A researcher aims to investigate if hospital A has a lower survival rate than hospital B when it comes to heart transplants? Test at the .02 significance level.

Hospital A: 420 survived; sample size = 600

Hospital B: 820 survived; sample size = 1000

What are the null and alternative hypotheses?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value of the test statistic?

What is the calculated (computed) value of the test statistic?

What is the p-value based on the computed test statistic?

State the decision rule and what is your conclusion?

(10 points) Q8. A company claims that its candy bars have exactly 4.00 grams of fiber. You have been asked by a competitor to test this claim at a significance level of .01. Sample evidence: n = 27 bars; sample mean is 4.13 grams of fiber; sample standard deviation is .28 grams of fiber.

What are the null and alternative hypotheses?

Draw the picture of the distribution of the test statistic. Include region (s) of rejection and non- rejection.

What is the critical value of the test statistic?

What is the calculated (computed) value of the test statistic?

What is the p-value based on the computed test statistic?

State the decision rule and what is your conclusion?

Construct 95% confidence interval estimate for the population mean

(15 points) Q9. A researcher is interested in determining whether there is a relationship between number of packs of cigarettes smoked per day (X) and longevity (in years) (Y). Please look at the output of regression below and give short answers the following questions.

Is this regression significant? Why?

What is the coefficient of correlation? Interpret the coefficient of correlation.

What is the coefficient of determination? What can you say about the relationship between two variables?

What is the regression equation?

What is the Y-intercept of the linear equation? Interpret the Y-intercept of the linear equation

What is the slope of the linear equation? Interpret the slope of the linear equation

What is the test-statistic to test the significance of the slope? What is your conclusion? (5% significance level)

What is the test-statistic to test the significance of the coefficient of correlation? What is your conclusion? (5% significance level)

How long will one live who smokes 2.5 packs per day?

(Optional) Extra credits: use the information from the table provided. You are NOT required to calculate by hand. (5 points) The researcher is comparing the employee engagement scores of male and female employees selected randomly and performed a two-sample t-test. She is testing at a significance level of .05. Employee engagement scores range from 0 (completely disengaged) to 100 (completely engaged)

What are the null and alternative hypotheses?

What is the critical value of the test statistic?

What is the calculated (computed) value of the test statistic?

What is the p-value based on the computed test statistic?

State the decision rule and what is your conclusion?

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