A random sample of 49 measurements from a population with population standard deviation - 4 had a sample mean of x = 8. An independent random sample of 64 measurements from a second population with population standard deviation d₂-5 had a sample mean of ₂11. 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. O The standard normal distribution. Samples are independent, the population standard deviations are known, and the sample sizes are sufficiently large. O The student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The student's t. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. OH! H₂H₂ H₂ H₂H₂ ⒸHg! H₂H₂ H₂² H₂ H₂ ܕܐܐ * ܨ O Hol g = Mg: Mg1 (c) Compute- ₁-₂-[ Compute the corresponding sample distribution value. (Test the difference ₂-₂. Round your answer to two decimal places.) (d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.) (e) Conclude the test. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a=0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (f) Interpret the results. O Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. O Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. O Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. O Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. (9) Find a 99% confidence interval for ₁-₂ (Round your answers to two decimal places.) lower limit upper limit Explain the meaning of the confidence interval in the context of the problem. O At the 99% level of confidence, it appears that the difference between population means is between the lower limit and the upper limit. O At the 99% level of confidence, it appears that the difference between population means is equal to the upper limit. O At the 99% level of confidence, it appears that the difference between population means is below the lower limit. O At the 99% level of confidence, it appears that the difference between population means is above the upper limit.