### Question Description

I need help with a Statistics question. All explanations and answers will be used to help me learn.

1. Suppose you want to test the claim that μ _{1} > μ _{2}. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that ≠ . At a level of significance of , when should you reject H _{0}?

n _{1} = 18 n _{2} = 13

_{1} = 635 _{2} = 620

s _{1} = 40 s _{2} = 25

2. Suppose you want to test the claim that μ _{1} ≠ μ _{2}. Assume the two samples are random and independent. At a level of significance of α = 0.02, when should you reject H _{0}?

Population statistics: σ _{1} = 0.76 and σ _{2} = 0.51

Sample statistics: _{1} = 1.9, n _{1} = 51 and _{2} = 2.3, n _{2} = 38

3. Find the critical values, t _{0}, to test the claim that μ _{1} = μ _{2}. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that .

n _{1} = 25 n _{2} = 30

_{1} = 25 _{2} = 23

s _{1} = 1.5 s _{2} = 1.9

4.Find the weighted estimate, to test the claim that p _{1} > p _{2}. Use α = 0.01. Assume the samples are random and independent.

Sample statistics: n _{1} = 100, x _{1} = 38, and n _{2} = 140, x _{2} = 50

5.Find the critical value, t _{0}, to test the claim that μ _{1} < μ _{2}. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that .

n _{1} = 15 n _{2} = 15

_{1} = 22.97 _{2} = 25.52

s _{1} = 2.9 s _{2} = 2.8

6. Find the weighted estimate, to test the claim that p _{1} = p _{2}. Use α = 0.05. Assume the samples are random and independent.

Sample statistics: n _{1} = 50, x _{1} = 35, and n _{2} = 60, x _{2} = 40

7.Suppose you want to test the claim that μ _{1} ≠ μ _{2}. Assume the two samples are random and independent. At a level of significance of α = 0.05, when should you reject H _{0}?

Population statistics: σ _{1} = 1.5 and σ _{2} = 1.9

Sample statistics: _{1} = 30, n _{1} = 50 and _{2} = 28, n _{2} = 60

8.Construct a 95% confidence interval for μ _{1} – μ _{2}. Assume the two samples are random and independent. The sample statistics are given below.

Population statistics: σ _{1} = 1.5 and σ _{2} = 1.9

Sample statistics: _{1} = 25, n _{1} = 50 and _{2} = 23, n _{2} = 60

9.Find the standardized test statistic, z, to test the claim that p _{1} ≠ p _{2}. Assume the samples are random and independent.

Sample statistics: n _{1} = 1000, x _{1} = 250, and n _{2} = 1200, x _{2} = 195

10.Find the standardized test statistic to test the claim that μ _{1} = μ _{2}. Assume the two samples are random and independent.

Population statistics: σ _{1} = 1.5 and σ _{2} = 1.9

Sample statistics: _{1} = 29, n _{1} = 50 and _{2} = 27, n _{2} = 60

11.

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