Two samples are random and independent. Find the P-value used to test the claim that μ1 = μ2. Use α = 0.05. Population statistics: σ1 = 2.5 and σ2 = 2.8 Sample statistics: x1 = 12, n1 = 40 and x2 = 13, n2 = 35
A. 0.0526
B. 0.1052
C. 0.1138
D. 0.4020
The statistical software output for this problem is :
Two sample Z summary hypothesis test:
μ1 : Mean of population 1 (Std. dev. = 2.5)
μ2 : Mean of population 2 (Std. dev. = 2.8)
μ1 - μ2 : Difference between two means
H0 : μ1 - μ2 = 0
HA : μ1 - μ2 ≠ 0
Hypothesis test results:
| Difference | n1 | n2 | Sample mean | Std. err. | Z-stat | P-value |
|---|---|---|---|---|---|---|
| μ1 - μ2 | 40 | 35 | -1 | 0.61664414 | -1.6216809 | 0.1052 |
P-value = 0.1052
B)
Two samples are random and independent. Find the P-value used to test the claim that μ1...
Find the critical value to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that σ 2/1= σ2/2. Use α = 0.05. n1 = 15 n2 = 15 x1 = 25.74 x2 = 28.29 s1 = 2.9 s2 = 2.8
Find the standardized test statistic to test the claim that μ1 ≠ μ2. Assume the two samples are random and independent. Population statistics: σ1 = 0.76 and σ2 = 0.51 Sample statistics: x1 = 3.6, n1 = 51 and x2 = 4, n2 = 38
Suppose you want to test the claim that μ1 ≠ μ2. Assume the two samples are random and independent. At a level of significance of α = 0.05, when should you reject H0? Population statistics: σ1 = 1.5 and σ2 = 1.9 Sample statistics: x1 = 30, n1 = 50 and x2 = 28, n2 = 60 A. Reject H0 if the standardized test statistic is less than -1.645 or greater than 1.645. B. Reject H0 if the standardized test...
Find the standardized test statistic to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that σ 2 /1 = σ 2 /2 . n1 = 15 n2 = 13 x1 = 27.88 x2 = 30.43 s1 = 2.9 s2 = 2.8
Find the critical values, t0, to test the claim that μ1 = μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that σ 2 1 ≠ σ 2 2 . Use α = 0.05. n1 = 32 n2 = 30 x1 = 16 x2 = 14 s1 = 1.5 s2 = 1.9
Find the standardized test statistic, t, to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that two populations' variance is the same (σ21= σ22). n1 = 15 n2 = 15 x1 = 25.76 x2 = 28.31 s1 = 2.9 s2 = 2.8
22) Suppose you want to test the claim that μ1 > μ2. Two samples are randomly selected from each population. The sample statistics are given below. At a level of significance of α = 0.10, find the test statistic and determine whether or not to reject H0. (8.1) n1 = 35 n2 = 42 x1 = 33 x2 = 31 s1 = 2.9 s2 = 2.8 A) z = 3.06; Reject H0 and support the claim that μ1 > μ2...
Find the standardized test statistic to test the claim that μ1 ≠ μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that σ 2 /1 ≠ σ 2 /2 . n1 = 11 n2 = 18 x1 = 6.9 x2 = 7.3 s1 = 0.76 s2 = 0.51
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 80 n2 = 70 x1 = 104 x2 = 106 σ1 = 8.4 σ2 = 7.2 (a) What is the value of the test statistic? (Round your answer to two decimal places.) (b) What is the p-value? (Round your answer to four decimal places.)...
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that: a) x3 follows a gaussian distribution b) estimate mean value μ3 and variance σ3^2 c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)