A random sample of 49 measurements from a population with population standard deviation₁=4had a sample mean ofx₁=15.An independent random sample of64 measurementsfrom a second population with population standard deviation₂=5had a sample mean ofx₂=18.Test the claim that the population means are different. Use level ofsignificance 0.01.

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

• The student'st. We assume that both population distributions are approximately normal with unknown standard deviations.
• The standard normal distribution. Samples are independent, the population standard deviations are known, and the sample sizes are sufficiently large.
• The student'st. 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.

(b) State the hypotheses.

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

(c) Computex₁x₂.

x₁x₂=

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

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

(e) Conclude the test.

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

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

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

At the= 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.

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.

(g) Find a 99% confidence interval for₁₂.

(Round your answers to two decimal places.)

• lower limit=
• upper limit=

Explain the meaning of the confidence interval in the context of the problem.

At the 99% level of confidence, it appears that the difference between population means is below the lower limit.

At the 99% level of confidence, it appears that the difference between population means is above the upper limit.

At the 99% level of confidence, it appears that the difference between population means is between the lower limit and the upper limit.

At the 99% level of confidence, it appears that the difference between population means is equal to the upper limit.