A random sample of 49 measurements from a population with population standard deviation₁=5had a sample mean ofx₁=12.An independent random sample of64 measurementsfrom a second population with population standard deviation₂=6had a sample mean ofx₂=15.Test the claim that the population means are different. Use level ofsignificance 0.01.

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

(b) Find theP-value of the sample test statistic. (Round your answer to four decimal places.)

(c) Conclude the test.

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

(e) Interpret the results.

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

(f) Find a 99% confidence interval for₁₂.

(Round your answers to two decimal places.)

• lower limit=
• upper limit=

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

• 1. At the 99% level of confidence, it appears that the difference between population means is above the upper limit.
• 2. At the 99% level of confidence, it appears that the difference between population means is between the lower limit and the upper limit.
• 3. At the 99% level of confidence, it appears that the difference between population means is below the lower limit.
• 4. At the 99% level of confidence, it appears that the difference between population means is equal to the upper limit.