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The average income of 16 families who reside in a large city is $54,356 and the...

The average income of 16 families who reside in a large city is $54,356 and the standard deviation is $8256. The average income of 12 families who reside in a suburb of the same city is $46,512 with a standard deviation of $1311. At ? = 0.01, can it be concluded that the income of the families who reside within the city is greater than that of those who reside in the suburb? Assume the populations have equal variances and use the p-value method.

Solutions

Expert Solution

Given :

  

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ1​ = μ2​

Ha: μ1​ > μ2​

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

The p-value corresponding to df = 26 and t = 3.246 (using t - table or calculator)

p-value=0.0016

Since p=0.0016 < 0.05,the null hypothesis is rejected.

Hence it can be concluded that the income of the families who reside within the city is greater than that of those who reside in the suburb.

milcah answered 1 year ago
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