The null and alternate hypotheses are:
H_{0} : μ_{1} =
μ_{2}
H_{1} : μ_{1} ≠
μ_{2}
A random sample of 12 observations from one population revealed a sample mean of 24 and a sample standard deviation of 3.8. A random sample of 8 observations from another population revealed a sample mean of 28 and a sample standard deviation of 3.7.
At the 0.01 significance level, is there a difference between the population means?
State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)
Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)
Compute the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
State your decision about the null hypothesis.
Do not reject H_{0}.
Reject H_{0}.
The p-value is
between 0.05 and 0.02
less than 0.001
between 0.05 and 0.1
between 0.001 and 0.01
between 0.1 and 0.2
The statistical software output for this problem is:
Hence,
a) Decision rule:
Reject Ho if |t| > 2.878
Reject Ho if t < -2.878 or t > 2.878
b) Pooled estimate = 14.148
c) Test statistic = -2.330
d) Do not reject Ho
e) between 0.05 and 0.02
c) Test statistic = -2.330
d)
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