I would like every question answered.
Section A 20 marks Answer all questions in this section. Topics: - Estimation of the mean and proportion and Hypothesis Testing Question 1 (10 marks) a) You, the district sales manager for a fast-food company prefer to compare sales performance in terms of standardized values. You recently hired a new analyst, and you decided to demonstrate to her how to standardize the value x = 15 given = 9 and = 5. Show the working you demonstrated to the new analyst. (2 marks) b) Based on your knowledge on the z statistic and the t statistic, a confidence interval inappropriately using a z-statistic instead of the tstatistic will give a wider, or narrower interval? Why? (2 marks) c) The manager of John’s supermarket received complaints from Cashiers at the supermarket that many customers who used the express checkout lane have more than the stipulated number of items for the lane. The express check-out lanes are limited to customers purchasing 10 or fewer items. A recently taken random sample of 25 customers entering express lanes at this supermarket found that 14 of them had more than 10 items. i. (i) Construct a 95% confidence interval for the percentage of all customers at this supermarket who enter express lanes with more than 10 items (4 marks) i. ii. (ii) Give a complete interpretation for the 99% confidence interval from part (i) (2 marks) Question 2 (10 marks) a) Define what is a null and alternative hypothesis? (2 marks) b) Your manager is interested in knowing whether nor not spending more money on digital advertising will lead to increased sales. Assist your manager by identifying a null and alternative statement based on this scenario. (2 marks) c) What does the level of significance tell you? (1 marks) d) How does one commit a type 1 error? (1 marks) e) Briefly explain the difference between a two-tailed and a one-tailed test (2 marks) f) Draw a two-tailed normal distribution curve with a significance level of 5%. On your graph identify the critical values, shade the rejection regions, and show alpha. (2 marks) Section B 40 marks In this section, you are required to answer two (2) questions only. Section B(i) - Answer either question one (1), or question two (2) Section B(ii) - Answer either question three (3) or question four (4) Topics: - Estimation & Hypothesis Testing: Two Populations; Chi-Square Tests; Analysis of Variance and Simple Linear Regression Section B(i) Question 1 (20 marks) Quack Fast Food Company Limited hired two chemists, Mr. Morris and Mr. Logan to produce their signature sauce. Mr. Smith, their boss, is not pleased with Mr. Logan’s attitude to work, so he is contemplating firing Mr. Logan and keeping Mr. Morris only to perform this job. The problem, however, is that Mr. Logan seems to produce a higher quality sauce whenever he oversees production when compared to Mr. Morris. Before making a final decision, Mr. Smith decided to collected data measuring the quality of different batches of sauce produced by Mr. Morris and Mr. Smith to make a better-informed decision. The results, measured on a quality scale, are listed below: Name Average Standard Deviation Sample Size Mr. Logan 98 1 8 Mr. Morris 94 4 10 a) Based on this data above, advise Mr. Smith whether Mr. Logan is better at making the signature sauce than Mr. Morris by using hypothesis testing – use the critical value approach with a level of significance at 5%. b) At the 99% level of confidence, can Mr. Smith conclude that the mean quality score for the sauce is above 90? Question 2 (20 marks) a) List two (2) types of chi-square test and explain the difference between both tests. (2 marks) b) How do you find a chi-square value in the left tail of the distribution? (2 marks) c) What is the parameter of a chi-square test? (1 mark) d) Consider the following contingency table, which records the results obtained for four samples of fixed sizes selected from four populations. Population 1 Population 2 Population 3 Population 4 Row 1 25 80 60 120 Row 2 45 65 90 70 i. Write the null and alternative hypotheses for a test of independence for this table.
(2 marks) ii. Calculate the expected frequencies for all cells assuming that the null hypothesis is true. (4 marks) iii. For alpha = .05, find the critical value of X2. Show the rejection and non-rejection regions on the chi-square distribution curve.
(5 marks) iv. Find the value of the test statistic X2.
(2 marks) v. Using alpha = .05, would you reject the null hypothesis? (2 marks) Section B(ii) Question 3 (20 marks) Surfer Dude Swimsuit Company plans to produce a new line of quick-dry swimsuits. Five textile companies are competing for the company’s quick-dry fabric contract. To check the fabrics of the five companies, Surfer Dude selected 10 random swatches of fabric from each company, soaked them with water, and then measured the amount of time (in seconds) each swatch took to dry when exposed to sun and a temperature of 80 F. The following table contains the amount of time (in seconds) each of these swatches took to dry. Company Time in seconds A 756 801 750 777 772 768 812 770 743 824 B 791 696 761 760 741 810 770 823 815 845 C 773 794 773 740 780 801 794 719 776 743 D 760 723 699 756 834 791 742 739 801 724 E 763 699 753 744 793 799 803 812 796 807 You are required to conduct a hypothesis test using the ANOVA method to decide whether the mean drying times for all fabrics produced by the five companies are the same. Use excel to produce the ANOVA output. Note: Summit a copy of the ANOVA output with your answer. a) Write the null and alternative hypotheses. (2 mark) b) What are the degrees of freedom for the numerator and the denominator? (2 marks) c) What are the values for the SSB, SSW, and SST. (3 marks) d) Show the rejection and non-rejection regions on the F distribution for α = 0.05. Shade the rejection region. (2 mark) e) Show the between-samples and within-samples variances. (2 marks) f) From the ANOVA output calculate the MSB and MSW (2marks) g) What is the critical value of F for α = .05? (1 marks) h) What is the calculated value of the test statistic F? (3 marks) i) Will you reject the null hypothesis stated in part a) at a significance level of 5%? Give a complete statement pertaining to the decision. (3 mark) Question 4 (20 marks) The Apparel Co. Ltd. has been using television advertisements to advertise their new clothing line for the past 12 months. The sales manager wants to assess the effect of these advertisements on sales for the last 12 months. You are to consider sales amount as the dependent variable and the number of advertisements as the independent variable. The sales amount (in ‘000) and the number of advertisements are shown below. Monthly Sales and Advertising at The Apparel Co. Ltd Month No of Advertisements Amount in sales in ‘000 1 19 60 2 23 78 3 30 69 4 24 71 5 20 83 6 26 74 7 34 99 8 36 100 9 25 64 10 31 98 11 27 81 12 27 77 Using excel, complete the following tasks: Note: Summit a copy of the regression output with your answer. a) Show the above data on a scatter plot and include the regression line. Label the graph and line completely (4 marks) b) What is the average sales across all months of advertising? (1mark) c) Identify r-squared on the regression output and interpret what it means in this scenario. (3 marks) d) Identify the 95% confidence interval for B (2 marks) e) Identify the 99% confidence interval for B (2 marks) f) Identify the standard deviation of error at the 1% level of significance (1 mark) g) Test at the 1% significance level whether the slope of the regression line is positive. Identify all steps in your analysis and make a complete and relevant decision. (7 marks) THE END! Semester 2, 2021/2022 MGMT301. A-St Hilaire Semester 2, 2021/2022 MGMT301. A-St Hilaire Semester 2, 2021/2022 MGMT301. A-St Hilaire