Question

A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 3. An independent random sample of 64 measurements from a second population had a sample mean of 18, with sample standard deviation 4. Test the claim that the population means are different. Use level of significance 0.01.

(a) What distribution does the sample test statistic follow? Explain.

The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.    

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

(b) State the hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂

H₀: μ₁ ≠ μ₂; H₁: μ₁ = μ₂    

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(c) Compute

x₁ − x₂.

x₁ − x₂ =

Compute the corresponding sample distribution value. (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


(d) Estimate the P-value of the sample test statistic.

P-value > 0.500

0.250 < P-value < 0.500    

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050 P-value < 0.010

(e) Conclude the test.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret the results.

Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.      Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means

Answer 1