Hi please can I get some help with these questions
QUESTION 1 In testing whether the means of two populations are equal, we are given the summary statistics calculated from two independent samples as follows: 111:26 \"2:26 :21 = 7.30 :22 = 6.80 51 = 1.05 52 = 1.20 Assuming that the population variances are equal, which one of the following statements is correct? 1. The two independent samples are not normally distributed. The pooled variance is equal to 0.3189. The standard error of the sample mean difference 31 i; is equal to 1.2713. The critical value for a two-tailed test at the 5% level of significance is 1.676. WPWN The rejection region at 5% level of significance is r > 2.009. QUESTION 2 A company wants to compare the mean number of days of sick leave for two classes of employees, those with less or equal to five years of service versus those with more than five years of service. The sample sizes are :11 = r12 = 100 employees. the sample means are E; = 241 and E; = 240 and the standard deviations of the two populations are 0': = 8.2 days and 0'2 = 5.7 days. The manager wantto test the hypotheses: Hg : pl 5 #2 against H1 : #1 5 11;. The p-value from the population difference in mean number of days of sick leave is equal to 1. 0.1587 2. 0.8413 3. 1.00 4. 0.3174 5. 0.9986 Consider two samples of data drawn from two independent populations that are normally distrib uted. The summary statistics are given below X1 = 57 *2 = 63 01 = 11.5 02 = 15.2 n1 = 20 n2 = 20 The analyst wants to test whether the population means differ at the 5% level of significance. Which one of the following statements is incorrect? 1. The hypotheses are: Ho : M1 - /2 = 0 VS H1 : /41 - /2 / 0. 2. The standard error of # 1 - M2 is 4.262. 3. The test statistic is = -1.4078. 4. The rejection region is [z| > z = 1.96. 5. Conclusion: Ho is rejected at the 5% level of significance. QUESTION 4 Refer to the information given on question 3, the p-value is 1. 0.1586 2. 0.9207 3. 0.0808 4. 0.0793 5. 0.0193 QUESTION 5 Two random samples of 10 observations are drawn from two independent populations that are normally distributed. Consider the following summary statistics under the assumption that the two population variances are unknown but equal. X1 = 249 *2 = 272 $1 = 35 $2 = 23 The 90% confidence interval for the difference between the two normal population means is 3 1. (-23 ; 38.1159) 2. (-57.1693 ; 11.1693) 3. (-45.9649 ; -0.0351) 4. (15.1159 ; 61.1159) 5. (-59.1519 ; 13.1519)
