(a)
To explain:whether the two sample variances are reasonable to use common population variance
(a)
Answer to Problem 10.24E
The obtained value is less than 3; therefore it is reasonable to use common population variance.
Explanation of Solution
Given:
D | E | F |
t-Test: Two-sample Assuming Equal Variances | ||
Sample 1 | Sample 2 | |
Mean | 28.667 | 28.286 |
Variance | 5.067 | 2.238 |
Observations | 6 | 7 |
Pooled Variance | 3.524 | |
Hypothesized Mean Difference | 0 | |
df | 11 | |
t Stat | 0.365 | |
P(T<=t) one-tail | 0.361 | |
t Critical one-tail | 1.796 | |
P(T<=t) two-tail | 0.722 | |
t Critical two-tail | 2.201 |
Calculation:
To test the common population variance is reasonable or not, we have the test statistics as
From the output by substituting the values we get
This value is less than 3 so it is reasonable to use common population variance.
Conclusion: The obtained value is less than 3, therefore it is reasonable to use common population variance.
(b)
To find: the observed value of the test statistic andthe P-value associated with the test
(b)
Answer to Problem 10.24E
The observed value for the test statistics is
Explanation of Solution
Given:
D | E | F |
t-Test: Two-sample Assuming Equal Variances | ||
Sample 1 | Sample 2 | |
Mean | 28.667 | 28.286 |
Variance | 5.067 | 2.238 |
Observations | 6 | 7 |
Pooled Variance | 3.524 | |
Hypothesized Mean Difference | 0 | |
df | 11 | |
t Stat | 0.365 | |
P(T<=t) one-tail | 0.361 | |
t Critical one-tail | 1.796 | |
P(T<=t) two-tail | 0.722 | |
t Critical two-tail | 2.201 |
Calculation:
From the above output the observed value for the test statistics is
The P-value associated with the test statistics for two tailed test is
The observed value for the test statistics is
Conclusion:
Therefore, observed value for the test statistics is
(c)
To find: the pooled estimate
(c)
Answer to Problem 10.24E
The pooled estimate
Explanation of Solution
Given:
D | E | F |
t-Test: Two-sample Assuming Equal Variances | ||
Sample 1 | Sample 2 | |
Mean | 28.667 | 28.286 |
Variance | 5.067 | 2.238 |
Observations | 6 | 7 |
Pooled Variance | 3.524 | |
Hypothesized Mean Difference | 0 | |
df | 11 | |
t Stat | 0.365 | |
P(T<=t) one-tail | 0.361 | |
t Critical one-tail | 1.796 | |
P(T<=t) two-tail | 0.722 | |
t Critical two-tail | 2.201 |
Calculation:
From the table, the pooled estimate
Conclusion: Thus, the pooled estimate
(d)
To state: conclusions about the difference in the two populations by using part b answer
(d)
Answer to Problem 10.24E
From part b we can see that the test statistics value is not lie in the critical region we fail to reject the null hypothesis that the population means are equal.
Explanation of Solution
Calculation:
t-critical value for the two-tail is 2.201
From part b we can see that the test statistics value is not lie in the critical region we fail to reject the null hypothesis that the population means are equal.
Conclusion: therefore, from part b we can see that the test statistics value is not lie in the critical region we fail to reject the null hypothesis that the population means are equal.
(e)
To find: a 95% confidence interval for the difference in the population and explain whether the interval confirm the conclusion in part d
(e)
Answer to Problem 10.24E
The 95% confidence interval for the difference in the population mean is
Explanation of Solution
Given:
D | E | F |
t-Test: Two-sample Assuming Equal Variances | ||
Sample 1 | Sample 2 | |
Mean | 28.667 | 28.286 |
Variance | 5.067 | 2.238 |
Observations | 6 | 7 |
Pooled Variance | 3.524 | |
Hypothesized Mean Difference | 0 | |
df | 11 | |
t Stat | 0.365 | |
P(T<=t) one-tail | 0.361 | |
t Critical one-tail | 1.796 | |
P(T<=t) two-tail | 0.722 | |
t Critical two-tail | 2.201 |
Calculation:
The 95% confidence interval for the difference in the population mean is
From the above output by substituting the value, we get
From the interval we can see that the interval contains 0 value so the interval conforms the conclusion in part d.
Conclusion: Therefore, 95% confidence interval for the difference in the population mean is
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Chapter 10 Solutions
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