QUESTION 5 Historically, the average waiting time spent in a queue on Friday afternoon at a bank's city branch was 10 minutes. To determine whether their new multi-queuing system constitutes an improvement, a random sample of 15 customers was taken and their waiting time recorded. The results are in the X1 column of the data file P14.12 which can be found in a folder under the CML Quizzes tab. Assume the distribution of waiting times is normally distributed. 1. State the direction of the alternative hypothesis used to test whether there is an improvement in average waiting time. Type gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as required in the box. 2. Calculate the test statistic correct to three decimal places (hint: use Descriptive Statistics to calculated the standard deviation and sample mean). 3. By referring to the appropriate Z or t-table, which of the following four given numbers is most likely to be the actual p-value for the test? Namely, 0.0814, 0.0515, 0.4292 or 0.4306. Enter your chosen number as your answer, using all four decimal places. 4. Is the null hypothesis rejected for this test if a 5% level of significance is used? Type yes or no. 5. Regardless of your answer for 4, if the null hypothesis was rejected, can we conclude that the average waiting time has improved with the new queuing system? Type yes or no.A B C D E 6 57 10.4 143 68 9.6 147 74 9.8 128 81 8.4 119 data file 10 82 8.8 130 11 86 8.9 135 P14.12 12 101 8.1 141 13 112 7.6 123 14 114 7.8 121 15 119 7.4 129 16 124 6.4 135 17QUESTION 7 A Brisbane warehouse buys prepacked bulk bags of Bundaberg Sugar with an advertised mean weight of 20 kilograms. To determine the validity of the advertised claim, the warehouse manager took a random sample of forty packets from the latest shipment received and found an average weight of the packets of 19.988 kilograms. Bundaberg Sugar know, from analysing data over many years. that their 20kg bulk bag packing process results in a standard deviation of 50 grams. 1. State the direction of the alternative hypothesis used to test the advertised claim. Type the letters gt (greater than), ge (greater than or equal to), It [less than}, le [less than or equal to) or ne {not equal to) as appropriate in the box. 2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 5% level of significance. If there are two critical values. state only the positive value. 3. Calculate the test statistic. reporting your answer to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. If it is shown later that the \"true" average weight of the bags was only 19.990 kilograms, determine the nature ofthe decision made in the test. Type cd {correct decision}, 'I [a Type I error was made} or 2 {a Type II error was made} as appropriate. 6. Regardless of your answer for 4, if the null hypothesis was rejected, would Bundaberg Sugar's advertised claim be valid at the 5% level of significance? Type yes or no. QUESTION 6 The Colgate company believes its toothpaste is more effective than its leading rival, Aim, in fighting tooth decay. A small scale clinical trial was held with 20 patients using Colgate and 23 using Aim. The results showed that the mean and variance of the number of cavities for Colgate was 9.7 and 11.85, respectively, with the results for Aim being 11.9 and 9.22. It is assumed that the population variances are the same and the distribution of the number of cavities for both groups closely approximates a normal distribution. Use alpha = 0.05. 1. If the hypotheses are to be written in the form of the average ofAim minus the average of Colgate, what is the direction ofthe alternative hypothesis used to test Colgate's belief. Type the letters gt{greaterthan), ge {greater than or equal to), It {less than), |e{less than or equal to} or ne [not equal to} as appropriate in the box. 2. Determine the standard error for the difference between means, reporting your answer to three decimal places. 3. Calculate the test statistic, reporting your answer to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Regardless of your answer for 4, ifwe fail to reject the null hypothesis, can we conclude that Colgate's belief is valid at the 5% level of significance? Type yes or no. QUESTION 4 A member of the |slip Urban Renewal Taskforce claimed that more than three quarters of new homes in the region were built with family rooms. 1. State the direction ofthe alternative hypothesis used to test the taskforce claim. Type gt (greater than), ge (greater than or equal to). It (less than), le (less than or equal to} or ne (not equal to} as appropriate in the box. Another committee member. who did not originally believe the claim, took a random sample of 84 houses in the area to test the validity of the claim. He found that 68 of them had family rooms. 2. Use the tables in the textbook to determine the critical value ofthe test statistic using a 3% level of significance. Ifthere are two critical values, state only the positive value. 3. Calculate the test statistic. correct to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Regardless of your answer for4, ifthe null hypothesis was not rejected, can we conclude that more than three quarters of new homes in the region were built with family rooms at the 3% level of significance? Type yes or no