A survey of two local communities is conducted to see whether there is difference in themean lengths of unemployment. Sample information, Community A: sample mean =12.4months, s=3, n=15; Community B: sample mean =14.4 months, s=4, n=15. Is there asignificant difference? Assuming equal variances, state the null and alternative hypotheses,and test the null hypothesis, using a=0.05. Find p=values and a 95% confidence interval forthe difference.

Name: A survey of two local communities is conducted to see whether there i
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Description: A survey of two local communities is conducted to see whether there is difference in themean lengths of unemployment. Sample information, Community A: sample mean =12.4months, s=3, n=15; Community B: sample mean =14.4 months, s=4, n=15. Is there asi

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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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A survey of two local communities is conducted to see whether there is difference in the
mean lengths of unemployment. Sample information, Community A: sample mean =12.4
months, s=3, n=15; Community B: sample mean =14.4 months, s=4, n=15. Is there a
significant difference? Assuming equal variances, state the null and alternative hypotheses,
and test the null hypothesis, using a=0.05. Find p=values and a 95% confidence interval for
the difference.

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Step 1

As per Bartleby guidelines , we are allowed to answer three sub parts. Thanks

Since Both the samples are Independent as two different local communities :

The provided sample means are shown below:

$\bar X_1 = 12.4$

$\bar X_2 = 14.4$

Also, the provided sample standard deviations are:

$s_1 = 3$

$s_2 = 4$

and the sample sizes are $n_1 = 15$ and $n_2 = 15$

1 ) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: $\mu_1$ - $\mu_2$

Ha: $\mu_1$ $\mu_2$

This corresponds to a two-tailed test, for which a t-test for two population means will be used.

Rejection Region

Based on the information provided, the significance level is $\alpha = 0.05$ , and the degrees of freedom are $df = 28$ In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is $t_c = 2.048$ , for $\alpha = 0.05$ and $df = 28$

The rejection region for this two-tailed test is $R = {t : ∣ t ∣ > 2.048}$

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