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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Since Both the samples are Independent as two different local communities :
The provided sample means are shown below:
Also, the provided sample standard deviations are:
and the sample sizes are and
1 ) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: - = 0( There is no significant difference in the mean lengths of unemployment)
Ha:
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 , and the degrees of freedom are 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 , for and
The rejection region for this two-tailed test is
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