A random sample of 15 observations from the first population revealed a sample m
ID: 3309518 • Letter: A
Question
A random sample of 15 observations from the first population revealed a sample mean of 314 and a sample standard deviation of 13. A random sample of 21 observations from the second population revealed a sample mean of 302 and a sample standard deviation of 10.
At the 0.05 significance level, is there a difference in the population means?
State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.)
Compute the pooled estimate of the population variance. (Round the final answer to 2 decimal places.)
The null and alternate hypotheses are:Explanation / Answer
Result:
The null and alternate hypotheses are:
A random sample of 15 observations from the first population revealed a sample mean of 314 and a sample standard deviation of 13. A random sample of 21 observations from the second population revealed a sample mean of 302 and a sample standard deviation of 10.
At the 0.05 significance level, is there a difference in the population means?
a.
State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.)
The decision rule is to reject H0 if t < -2.032 or >2.032 .
This is a (Click to select)two tailed test.
b.
Compute the pooled estimate of the population variance. (Round the final answer to 2 decimal places.)
Pooled estimate of the population variance 128.41
c.
Compute the test statistic. (Round the final answer to 3 decimal places.)
The test statistic is: t = 3.132.
d.
What is your decision regarding H0?
H0 is (Click to select) rejected.
e.
Estimate the p-value. (Round the final answer to 4 decimal places.)
The p-value is 0.0036 .
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
15
Sample Mean
314
Sample Standard Deviation
13
Population 2 Sample
Sample Size
21
Sample Mean
302
Sample Standard Deviation
10
Intermediate Calculations
Population 1 Sample Degrees of Freedom
14
Population 2 Sample Degrees of Freedom
20
Total Degrees of Freedom
34
Pooled Variance
128.4118
Standard Error
3.8309
Difference in Sample Means
12.0000
t Test Statistic
3.1324
Two-Tail Test
Lower Critical Value
-2.0322
Upper Critical Value
2.0322
p-Value
0.0036
Reject the null hypothesis
The null and alternate hypotheses are:
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