Consider two independent samples: Sample 1 has 217 observations and Sample 2 has 440 observations. In testing H0: (mu2 - mu1) = 0 versus H1: (mu2 - mu1) LaTeX: \ne≠ 0, a t test statistic of -3.111 with 400 degrees of freedom are correctly computed. What is the P-value? (Answer as a probability, not a percent. Record your answer accurate to at least the nearest third decimal place with standard rounding.) .
P value =0.002.......................by using Excel command =TDIST(ABS(-3.111),400,2)
Consider two independent samples: Sample 1 has 217 observations and Sample 2 has 440 observations. In...
a sample of 113 observations indicated that X1 is 71. A second sample of 157 observations indicated that X2 is 95. Conduct a z-test of hypothesis about a difference in population proportions using a 0.03 significance level. H0: p1 - p2 ≥ 0 H1: p1 - p2 < 0 a)State the decision rule.Reject H0 in favour of H1 if the computed value of the statistic is less than -1.88 or greater than 1.88.Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.17.Reject H0 in favour of H1 if the computed...
A sample of 8 observations from the population indicated that sample variance s12 is 441. A second sample of 8 observations from the same population indicated that sample variance s22 is 121. Conduct the following test of hypothesis using a 0.1 significance level. H0: σ12 = σ22 H1: σ12 ≠ σ22 You should use the tables in the book for obtaining the F values. For full marks your answer should be accurate to at least two decimal places. a) State...
Independent random samples of size n1=38 and n2=86 observations, were selected from two populations. The samples from populations 1 and 2 produced x1=18 and x2=13 successes, respectively. Define p1 and p2 to be the proportion of successes in populations 1 and 2, respectively. We would like to test the following hypotheses: H0:p1=p2 versus H1:p1≠p2 (a)To test H0 versus H1, which inference procedure should you use? A. Two-sample z procedure B. One-sample z procedure C. One-sample t procedure D. Two-sample t...
John has obtained two independent samples from two populations, where the sample statistics are shown in the table below. Assuming equal variances, he can construct a 95 percent confidence interval for the difference of the population means to be Sample 1 Sample 2 Mean 22.7 20.5 Variance (s^2) 5.4 3.6 Observations (sample size) 9 9 [0.08, 4.32] [1.17, 5.08] [2.44,6.19] [-0.09, 3.19] A corporate analyst is testing whether mean inventory turnover has increased. Inventory turnover in six randomly chosen product...
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2
) observations, where σ
2 > 0 is
unknown. Consider testing
H0 : σ
2 = σ
2
0 versus H1 : σ
2
6= σ
2
0
;
where σ
2
0
is known.
(a) Derive a size α likelihood ratio test of H0 versus H1. Your rejection region should
be written in terms of a sufficient statistic.
(b) When the null...
Independent random samples of n1 = 120 and n2 = 120 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 62 successes, and sample 2 had 67 successes. You wish to perform a hypothesis test to determine if there is a difference in the sample proportions p1 and p2. (a) State the null and alternative hypotheses. - H0: (p1 − p2) = 0 versus Ha: (p1 − p2) ≠ 0 - H0: (p1 − p2)...
Independent random samples of 180 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 104 successes, and sample 2 had 113 successes. Suppose that, for practical reasons, you know that p1 cannot be larger than p2. Test the appropriate hypothesis using α = 0.10. Given: H0: (p1 − p2) = 0 versus Ha: (p1 − p2) < 0 Solve: Find the test statistic. (Round your answer to two decimal places.) z = ?? Find the...
5. We have two independent samples of n observations X1,X2-…Xn and Yi,½, . …Ý, We want to test the hypothesis H0 : μ®-ty versus the alternative H1 : μζ μυ. (a) First, assume that the null hypothesis H0 is true and find the MLE for μ- - y. (b) Then plug this estimate into the log likelihood along with the MLBs μτ-x and μ to calculate the LRT statistic. (c) Is this likelihood ratio test equivalent to the test that...
5. We have two independent samples of n observations X1, X2, .. . , Xn and Yı, Y2,.. . , Yn We want to test the hvpothesis H 0 : μΧ-My versus the alternative H1 : μΧ * My (a) First, assume that the null hypothesis Ho is true and find the MLE for μ-Ac-My (b) Then plug this estimate into the log likelihood along with the MLE's μχ-x and My-- to calculate the LRT statistic (c) Is this likelihood...
Consider the following hypothesis test. The following results are from independent samples taken from two populations. H0: Ha: μ1 μ2 0 μ1 μ2 0 Sample 1 Sample 2 n1 35 n2 40 13.6 10.1 s1 5.2 s2 8.5 testSELF x ¯1 x ¯2 x ¯1 x ¯ a. What is the value of the test statistic? b. What is the degrees of freedom for the t distribution? c. What is the p-value? d. At α .05, what is your conclusion?