TASK DUE XXXXXXXXXX Question 01 A local health centre noted that in a sample of 400 patients, 80 were referred to them by the local hospital. a. Provide a 95% confidence interval for all the patients...

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TASK DUE 19.06.2020 Question 01 A local health centre noted that in a sample of 400 patients, 80 were referred to them by the local hospital. a. Provide a 95% confidence interval for all the patients who are referred to the health centre by the hospital. b. What sample size would be required to estimate the proportion of all hospital referrals to the health centre with a margin of error of 0.04 or less at 95% confidence? Question 02 The average starting salary of students who graduated from colleges of Business in 2009 was $48,400. A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $8000. We want to determine whether or not there has been a significant increase in the starting salaries. Step 1. Statement of the hypothesis Step 2. Standardised test statistic formula Step 3. State the level of significance Step 4. Decision Rule (Draw a bell to show rejection zone) Step 5. Calculation of the statistic Step 6. Conclusion Question 03 The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below. a. State the null and alternative hypothesis for single factor ANOVA. b. State the decision rule (α = 0.05). c. Calculate the test statistic. d. Make a decision. Question 04 Personal wealth tends to increase with age as older individuals have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and records their total wealth (Y) and their current age (X). a. State the estimated regression line and interpret the slope coefficient. b. What is the estimated total personal wealth when a person is 50 years old? c. What is the value of the coefficient of determination? Interpret it. d. Test whether there is a significant relationship between wealth and age at the 10% significance level. Perform the test using the following six steps. Step 1. Statement of the hypotheses Step 2. Standardised test statistic Step 3. Level of significance Step 4. Decision Rule Step 5. Calculation of test statistic Step 6. Conclusion Question 05 A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. a. Write out the estimated regression equation for the relationship between the variables. b. Compute coefficient of determination. What can you say about the strength of this relationship? c. Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance. d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.