A random sample of 49 measurements from one population had a sample mean of 16, with a sample standard deviation of 5. An independent random sample of 64 measurements from a second population had a sample mean of 19, with a sample standard deviation of 6. Test the claim that the population means are different. Use a level of significance of 0.01.
(a) What distribution does the sample test statistic follow? Explain.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
(b) State the hypotheses.
H0: μ1 = μ2; H1: μ1 ≠ μ2
(c) Compute x1 - x2.
x1 - x2 =
Compute the corresponding sample distribution value. (Test the difference μ1 - μ2. Round your answer to three decimal places.)
(d) Estimate the P-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
(e) Conclude the test.
At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret the results.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.