Question

The *MINITAB* printout shows a test for the difference in
two population means.

Two-Sample
T-Test and CI: Sample 1, Sample 2 |
||||

Two-sample T for Sample 1 vs Sample 2 | ||||

N | Mean | StDev | SE Mean | |

Sample 1 | 5 | 29.00 | 3.00 | 1.3 |

Sample 2 | 7 | 28.89 | 3.63 | 1.4 |

Difference = mu (Sample 1) - mu (Sample 2) | ||||

Estimate for difference: 0.11 | ||||

95% CI for difference: (-4.3, 4.5) | ||||

T-Test of difference = 0 (vs not =): | ||||

T-Value = 0.06 P-Value
= 0.96 DF = 10 |
||||

Both use Pooled StDev = 3.39 |

(a) Do the two sample standard deviations indicate that the assumption of a common population variance is reasonable?

Yes, the ratio of the two variances is less than three.Yes, the ratio of the two variances is more than three. No, the ratio of the two variances is less than three.No, the ratio of the two variances is more than three.It is not possible to check that assumption with the given information.

(b) What is the observed value of the test statistic?

*t* =

What is the *p*-value associated with this test?

*p*-value =

(c) What is the pooled estimate *s*^{2} of the
population variance? (Round your answer to two decimal
places.)

*s*^{2} =

(d) Use the answers to part (b) to draw conclusions about the
difference in the two population means. (Use *?* =
0.10.)

Since the *p*-value is greater than 0.10, the results are
significant. There is sufficient evidence to indicate a difference
in the two population means.Since the *p*-value is less than
0.10, the results are not significant. There is insufficient
evidence to indicate a difference in the two population
means. Since the *p*-value is less
than 0.10, the results are significant. There is sufficient
evidence to indicate a difference in the two population means.Since
the *p*-value is greater than 0.10, the results are not
significant. There is insufficient evidence to indicate a
difference in the two population means.

(e) Find the 95% confidence interval for the difference in the
population means.

to

Does this interval confirm your conclusions in part (d)?

Yes, since 0 falls in the confidence interval, there is sufficient evidence to indicate a difference in the two population means.Yes, since 0 falls in the confidence interval, there is insufficient evidence to indicate a difference in the two population means. Yes, since 0 falls outside the confidence interval, there is sufficient evidence to indicate a difference in the two population means.No, since 0 falls in the confidence interval, there is sufficient evidence to indicate a difference in the two population means.No, since 0 falls outside the confidence interval, there is insufficient evidence to indicate a difference in the two population means

Answer #1

(a)

Correct option:

Yes, the ratio of the two variances is less than three.

(b) Observed test statistic is:

t = 0.06

p-value = 0.96

(c) s^{2} = 3.39^{2} = 11.4921

(d)

Correct option:

Since p-value is greater than 0.10 the results are not significant. There is insufficient evidence to indicate a difference in the two population means.

(e)

95% Confidence interval for the difference in the population means:

(-4.3,4.5)

Correct option:

Yes, since 0 falls in the confidence interval, there is insufficient evidence to indicate difference in population means.

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