STA1502 TRIAL EXAMINATIO N PAPER 2022 (Questions and Answers)

STA1502 TRIAL EXAMINATIO N PAPER 2022 (Questions and Answers) Assume that you have a sample of n1 D 9; with the sample mean XN1 D 42 and a sample standard deviation of S1 D 4; and you have an independent sample of n2 D 17 from another population with a sample mean of XN2 D 34 and the sample standard deviation S2 D 5: Test the hypothesis that the population mean for group 1 is greater than the population mean for group 2. Which one of the following statements is incorrect? 1. There are two independent populations and the test statistic ist–test. 2. The null nad alternative hypothesis are: H0 : 1 2 D 0 vs H1 : 1 > 2 : 3. The critical value at 1% level is 2:492: 4. The test statistic is 4:1375: 5. Do not reject H0 at the 1% level of significance. Question 2 Consider the information on question 1, the 95% confidence interval estimate for the difference between the two population means is 1. .4:0092I 11:9908/ 2. .4:2103I 11:7897/ 3. .8I 3:7897/ 4. .4:0092I 10:9098/ 5. . 11:9908I 4:0092/ Question 3 Suppose the necessary conditions are met, the population variances are known, and a two-tailed test is being conducted to test the difference between two population means . 1 2 /. Given the following information Sample A: n A D 30 XNA D 53:469 and 2 A D 374 Sample B: nB D 32 XNB D 48:625 and 2 B D 106 Test the hypothesis to determine if the population means are the same at D 0:05 2 STA1502/103 Which one of the following statements is incorrect? 1. The pooled variance for the test statistic is not valid. 2. If the two populations are normally distributed than the difference between the two populations means is also normally distributed. 3. The standard error for the difference XNA XNB is 3:9723: 4. The rejection region is Z < 1:22 and Z > 1:22: 5. The test statistic Z D 1:2189: Question 4 In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows: Population 1 2 Sample size n1 D 26 n2 D 26 Sample mean xN1 D 7:30 xN2 D 6:80 Sample variance s 2 1 D .1:05/ 2 s 2 2 D .1:20/ 2 Assume that the population variances are equal. Which one of the following statements is incorrect? 1. The t–test statistic is appropriate 2. The rejection region at 5% is t > t.50I0:05/ D 1:676 3. The standard error of XN1 XN2 D 0:3127 4. The critical value for a one–tailed test at 5% level of significance is 2:009 5. The 99% confidence interval for XN1 XN2 is . 0:3374I 1:3374/ Question 5 Six functionally illiterate adults were given an experimental one-week crash course in reading. Each of the six adults was given a reading test prior to the course and another test after the course. The results are shown below: Adult 1 2 3 4 5 6 Score after course 60 Score before course 28 3 Which one of the following statements is incorrect? 1. The distribution of paired difference is not normally distributed. 2. The rejection region at 1% level of significance is t > 3; 365 3. The test statistic t D 3:635 4. Reject H0 at 1% level of significance 5. LC L D 7:125 and UC L D 24:875 Question 6 Suppose that person A believes that sons, upon maturity, are in general taller than their fathers. Person B, on the other hand, argues that the opposite is true. In order to investigate this issue, we measure the height of a random sample of five father-son pairs. The following are the results (in cm): Pair 1 2 3 4 5 Son Father A statistical test (at the 5% significance level) is to be performed to solve this issue. The test statistic is 1. 1:5710 2. 1:7510 3. 0:8750 4. 2:7760 5. 1:8510 Question 7 A food processor wants to compare two preservatives for retarding spoilage. Suppose 16 cuts of fresh meat are treated with preservative A and 16 are treated with preservative B, and the number of hours until spoilage is recorded for each of the 32 cuts of meat. The results are summarised in the table below: Preservative A Preservative B Sample mean 108:7 98:7 Sample standard deviation 10:5 13:6 A food processor wants to infer at the5% significance level that the population variances differ. 4 STA1502/103 Which of the following statements below is correct? 1. H0 : 2 1 2 2 D 0 against H1 : 2 1 2 2 < 0: 2. The test statistic is 0:956: 3. The LC L D s 2 1 s 2 2 1 F0:025;15;15 D 1:705: 4. The UC L D s 2 1 s 2 2 F0:025;15;15 D 0:208: 5. We fail to reject the null hypothesis at D 0:05: Question 8 A random sample of households from community A is selected and the head of each household is asked if anyone in his community is bothered by noise pollution. 60 out of a sample of 180 in his community answered “yes”. A random sample of households from community B is selected. 75 out of a random sample of 200 in community B answered “yes”. The objective is to test if there is a difference in noise pollution in the two communities. Which of the following statements is incorrect? 1. bp1 D 0:3333 bp2 D 0:375 2. The pooled variance for proportion is 0:3553 3. The standard error of the estimate is 0:0024: 4. The critical value for the 90% confidence interval for the difference between p1 and p2 is 1:645: 5. The test statistic is 0:8476