A random sample of 49 measurements from one population had asample mean of 16, with sample standard deviation 3. An independentrandom sample of 64 measurements from a second population had asample mean of 18, with sample standard deviation 4. Test the claimthat the population means are different. Use level of significance0.01. (a) What distribution does the sample test statistic follow?Explain.
The standard normal. We assume that both populationdistributions are approximately normal with known standarddeviations. The Student's t. We assume that bothpopulation distributions are approximately normal with unknownstandard deviations.    The Student'st. We assume that both population distributions areapproximately normal with known standard deviations. The standardnormal. We assume that both population distributions areapproximately normal with unknown standard deviations.
(b) State the hypotheses.
H0: μ1 ≠μ2; H1:μ1 =μ2H0:μ1 = μ2;H1: μ1 ≠μ2    H0: μ1 =μ2; H1:μ1 <μ2H0:μ1 = μ2;H1: μ1 >μ2
(c) Compute
x1 − x2.
x1 − x2 =
Compute the corresponding sample distribution value. (Test thedifference μ1 − μ2. Roundyour answer to three decimal places.)
