Discuss the below:
Q1 A sample of 40 observations is selected from one population. The sample mean is 102 and the sample STDEV is 5. A second sample of 50 observations is selected from a second population. That sample mean is 99 and the STDEV is 6. Conduct the following test of hypotheses using the 0.04 significance level:
H(0): m(1) = m(2)
H(1): m(1) is not equal to m(2)
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule.
c. Compute the value of the z- test statistic.
d. State your decision regarding H(0).
e. What is the p-value?
Q2 The null and alternate hypotheses are:
H(0): m(1) = m(2)
H(1): m(1) is not equal to m(2)
A random sample of 10 observations from one sample revealed a sample mean of 23 and a sample STDEV of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample STDEV of 5. At the 0.05 significance level, is there a difference between the population means? Also,
(a) state the decision rule,
(b) compute the pooled estimate of the population variance,
(c) compute the t-test statistic,
(d) state your decision about the null hypothesis, and
(e) estimate the p-value.