QUESTION 1 a) A study claims that all customers spend an average of 32 minutes or more at the post office. A random samp

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Question 1 A A Study Claims That All Customers Spend An Average Of 32 Minutes Or More At The Post Office A Random Samp 1 (73.9 KiB) Viewed 40 times

Question 1 A A Study Claims That All Customers Spend An Average Of 32 Minutes Or More At The Post Office A Random Samp 2 (45.76 KiB) Viewed 40 times

Question 1 A A Study Claims That All Customers Spend An Average Of 32 Minutes Or More At The Post Office A Random Samp 3 (80.26 KiB) Viewed 40 times

QUESTION 1 a) A study claims that all customers spend an average of 32 minutes or more at the post office. A random sample of 18 customers showed that the mean time spent waiting in line to perform transaction at post office counters was 28 minutes with a standard deviation of 4 minutes. Assume that such waiting times for all customers are normally distributed. Testing at 5% signficance level, can you prove that the customers spend less than 32 minutes at the post office counter? (use critical value approach) (7 marks) b) A local authority requires all private cars to carry out periodic emission tests. There are only 2 emission test stations in a small town, A and B. Car owners complained lack of uniformity of proceduces at the two stations, resulting in different failure rates. A sample of 400 cars at Station A showed that 80 failed the test; a sample of 470 cars at Station B found that 75 failed the test. c) Test at a 5% signficance level, can you conclude that the two population proportions are different? (use p-value approach) Samples are taken from two batches of paint and the viscosity. The information is summarised below. Paint A B Sample mean (x) 114.2 115.3 Sample standard deviation (s) 0.62 0.94 (7 marks) Sample size (n) 4 6 Assuming that the two population are normally distributed and the population standard deviations are equal. Test at the 5% significance level, whether the mean viscosities of the two paints are equal. (9 marks)

QUESTION 2 a) Define the F Distribution. (4 marks) b) The following table lists the numbers of customer complaints received by the Head Office of a restaurant for three different chain outlets. LASES HB3 Outlet 1 4 9 12 3 11 8 13 Outlet 2 243386 13 Outlet 3 8 12 11 3 9 14 Using a 5% significance level, test the null hypothesis that the mean number of customer complaints received per day are the same for each of these three outlets. (16 marks)

Page View QUESTION 3 a) Shola Sdn Bhd sells products online. The company's management wants to find out if the number of orders received at the company's office on each of the 6 days of the week is the same. The company took a sample of 400 orders received for 4-week period, the frequency distribution for these orders are presented in the table below. Days of the week Number of orders received Undergraduates Before the course After the course A Read aloud | Add textDraw Test at the 1% significance level whether the null hypothesis that the orders are evenly distributed over all days of the week is true. (8 marks) 1 8 10 b) A university sent ten of its undergraduate students to attend a course in building self- confidence development. Assessment on the effectiveness of the course were conducted before and after students attended the course. The scores (on a scale of 1 to 15, 1-being the lowest and 15= being the highest score) are presented in the table below. 258 Mon 78 345 Tue Wed Thu Fri Sat 58 52 76 75 61 4 9 11 566 669 END OF QUESTION PAPER 7 759 867 9 7 10 102 9 Test at 2.5% significance level whether attending this course increases the mean score of the undergraduate students. (12 marks) (Total: 65 marks)