Homework SourseIf a random sample of 16 homes south of Center Street in Pro
If a random sample of 16 homes south of Center Street in Provo has a mean selling price of $145,100 and a standard deviation of $4525, and a random sample of 27 homes north of Center Street has a mean selling price of $148,575 and a standard deviation of $5725, can you conclude that there is a significant difference between the selling price of homes in these two areas of Provo at the 0.05 level? Assume normality.
(a) Find t. (Give your answer correct to two decimal places.)
(ii) Find the p-value. (Give your answer correct to four decimal places.)
(b) State the appropriate conclusion.
Solution
2 SAMPLE T TEST (UNPOOLED)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a 2 tailed test.
Calculating the means of each group,
X1 = 145100
X2 = 148575
Calculating the standard deviations of each group,
s1 = 4525
s2 = 5725
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 16
n2 = sample size of group 2 = 27
Thus, df = n1 + n2 - 2 = 41
Also, sD = 1579.125897
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -2.200584517 [ANSWER, PART A]
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where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = 2.01954097
Thus, comparing t and tcrit, we decide to WE REJECT THE NULL HYPOTHESIS.
Also, using p values,
p = 0.033455265 [ANSWER, PART A, II]
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we conclude that there is no significant difference between the selling price of homes in these two areas of Provo at the 0.05 level. [ANSWER, B]
