A random sample of 49 measurements from one population had a sample mean of14, with sample standard deviation5. An independent random sample of64 measurementsfrom a second population had a sample mean of17, with sample standard deviation6. 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.

• 1. 1 The Student'st. We assume that both population distributions are approximately normal with known standard deviations.
• 2. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
• 3. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
• 4. The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.

(b) State the hypotheses.

• H₀:₁=₂;H₁:₁>₂
• H₀:₁=₂;H₁:₁₂
• H₀:₁=₂;H₁:₁<₂
• H₀:₁₂;H₁:₁=₂

(c) Computex₁x₂ . x₁x₂=

(d) Compute the corresponding sample distribution value. (Test the difference₁₂. Round your answer to three decimal places.)

(e) Estimate theP-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

(f) Conclude the test.

• 1. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
• 2. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
• 3. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• 4. At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

(g) Interpret the results.

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

(h) Find a 95% confidence interval for₁₂.

(Round your answers to two decimal places.)

• lower limit=
• upper limit=

(i) Explain the meaning of the confidence interval in the context of the problem.

• 1. Because the interval contains only positive numbers, this indicates that at the 95% confidence level,₁>₂.
• 2. Because the interval contains both positive and negative numbers, this indicates that at the 95% confidence level,₁=₂.
• 3. We can not make any conclusions using this confidence interval.
• 4. Because the interval contains only negative numbers, this indicates that at the 95% confidence level,₁<₂.