Question

If a random sample of 24 homes south of a town has a mean selling price of $145,500 and a standard deviation of $4500, and a random sample of 21 homes north of a town has a mean selling price of $148,725 and a standard deviation of $5975, can you conclude that there is a significant difference between the selling price of homes in these two areas of the town at the 0.05 level? Assume normality.

(a) Find t. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)

Answer 1

The provided sample means are shown below:

,

Also, the provided sample standard deviations are:

,

and the sample sizes are n1​=24 and n2​=21.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

a)

Test Statistics

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

b)

The p-value is p = 0.0454

Graphically

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