Hello, please may I get some help

| QUESTION 1 Pg Printers is evaluating the delivery time of two courier delivery services in Johannesburg. Their initial belief is that there is no difference between the average delivery times of the two courier services. To examine this view, P Q Printers used both courier services daily on a random basis over a period of three months for deliveries to similar destinations. A dispatch clerk in the marketing department recorded delivery times. Courier A was used 60 times over this period and a sample mean delivery was 42 minutes. Courier B was used 48 times over the same period and their sample mean delivery time was 38 minutes. Consider the population standard deviation of the delivery times for courier A is 14 minutes, and for courier B is 10 minutes. Assume the delivery times are normally distributed. Which one of the following statements is correct? 1. The hypotheses are H0 : #1 = M vs H2 : #1 > #2. 2. The rejection region at 5% significance level is t > 1.96 or t > -1.96. 3. Z-test statistic is 1.37. 4. The 95% confidence interval for the delivery times is (0.53; 8.53). 5. The p-value for a two-tailed test is 0.0418. QUESTION 2 Consider the following hypotheses and the sample data drawn independently from two normally distributed populations: Ho:p1~#2=0 against H1:;11p2>0 A random sample of :11 = 20 is selected with a mean of 5'? and a second random sample of r12 = 21] is independently selected with a mean of 63. Assume that the two samples are normally distributed and the population standard deviations are 11.5 and 15.2 respectively. The analyst wants to test whether the population means differ at 5% significance level. The p-value is 1. 0.0793 2. 0.0808 3. 0.9207 4. 1.4078 5. 0.7930 QUESTION 3 A financial analyst wished to establish whether the mean return on investment per cent (Ftol%} of the financial companies is greater than the mean Rol% of the manufacturing companies. The financial analyst randomly sampled 28 financial companies and found their sample mean Flo|% to be 18.714 % with a standard deviation of 9.645%. For a random sample of 24 manufacturing companies, the sample mean Ftol% was 15.125 with a sample standard deviation of 8.823%. This information is summarized below Sample 1: Financial Sample 2: Manufacturing 711 = 28 :12 = 24 fl = 18.714 f2 = 15.125 31 = 9.645 S: = 8.823 Assuming that the population variances are equal, the 95% confidence interval for the difference between two population means is 1. (5.987; 12.098) 2. (3.589; 5.1838) 3. (0.9678; 4.657) 4. (-3.589; 8.7861) 5. (1.5948; 8.7728) QUESTION 4 A random sample of 10 home internet users was selected from Telkom's database and their monthly internet usage (in hours) was identified for March last year (period 1) and again for March this year (period 2). The data is shown in table below Periodl 70 85 64 83 68 91 65 78 96 92 Period 2 72 84 68 88 68 95[64 76 102 94 Suppose that Telkom's internet marketing manager asked the question: Is the internet usage in- creasing? To answer to this question, a statistics practitioner wants to conduct a hypothesis test, at the 5% significance level to determine if the monthly internet usage per user has increased significantly from period 1 (March last year} to period 2 (March this year). Which one of the following statements is incorrect? 1. This is a matched-pairs hypothesis test because the two samples period 1 and period 2 are drawn from the same subscribers. The hypotheses are H0 : 17 17 g 0 vs H1 : ,uD > 0. The degrees of freedom df is 9. The 95% confidence interval for matched-pairs samples is (-3.908 ; 0.108). The test statistic t = 21.407. $515390!\" QUESTION 5 The following table contains information on matched sample values upon which the differences calculated between the two samples are assumed to be normally distributed. Number 12345l678 Sample1 18 12 21 22 16 14 17 18 Sample2 21 ll 23 20 20 17 17 22 The EwTutor wants to test whether the mean difference differ from zero. Which one of the following statements is incorrect? 1. The hypothesis are: H0 : pg :0 vs H1 :pD 99 O. 2. The sample mean is (1.625) and the sample standard deviation is 2.3261. 3. The standard error is 0.8224. 4. The test statistic is -1.9759. 5. The rejection region at 1% is t > 4.9759. QUESTION 6 After a recent AIDS awareness campaign, the department of National Health commissioned a market research company to conduct a survey on its effectiveness. Their brief was to establish whether the recall rate of teenagers differed from that of young adults (20 - 30 years of age). The market research company interviewed a random sample of 640 teenagers and 420 young adults. It was found that 362 teenagers and 260 young adults were able to recall the AIDS awareness slogan of \"AIDS: don't let it happen\". The management wants to test, at the 5% level of significance, the null hypothesis H0 : There is an equal recall rate between teenagers and young adults. The test statistic is 1. 0.0316 2.0 163 1 .6906 a 1.6906 91??!\" 16.9870 QUESTION 7 A recent study claims that girls and boys do not perform the same on math tests taken from a grade 12. Suppose that in a representative sample, 344 of 430 girls and 369 of 450 boys score at proficient or advanced levels on a standardized math test. The principal wants to examine whether the proportion of girls who score at proficient or advanced levels differs from the proportion of boys at 5% level of significance. Which one of the following statements is incorrect? 1. 131 =03 and p2 =0.32. 2. The standard error for 51 - 132 is 0.0264. 3. The test statistic for ,61 - ,6; is -1.8519. 4. The hypotheses: Ho : P1 - P2 = 0 vs H1 : P1 - P2 913 0. 5. Conclusion: the proportion of girls who score at proficient or advanced levels does not differ significantly from the proportion of boys. QUESTION 8 Random samples from two normal populations produced the following statistics: sf=350 n1=31 S=700 \"2:31 a=0.05 Ho:a=a vs H1:a%>a The statistician wants to test the quality of the two population variances. The 95% confidence interval of ratio of two population variances is 1. (0.2415; 1.035) 2. (1.2415; 2.035) 3. (1.045; 0.3251) 4. (0.0241; 1.0035) 5. (0.8765; 3.9876)