If a random sample of 27 homes south of Center Street in Provo has a mean sellin
ID: 3134770 • Letter: I
Question
If a random sample of 27 homes south of Center Street in Provo has a mean selling price of $145,150 and a standard deviation of $4825, and a random sample of 27 homes north of Center Street has a mean selling price of $148,550 and a standard deviation of $6000, 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.)
Explanation / Answer
a)
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 two tailed test.
Calculating the means of each group,
X1 = 145150
X2 = 148550
Calculating the standard deviations of each group,
s1 = 4825
s2 = 6000
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 27
n2 = sample size of group 2 = 27
Thus, df = n1 + n2 - 2 = 52
Also, sD = 1481.748529
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -2.294586384 [ANSWER]
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ii)
Also, using p values,as this is 2 tailed,
p = 0.025824979 [ANSWER P VALUE]
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As P < 0.05, we reject Ho.
There is a significant difference between the selling price of homes in these two areas of Provo at the 0.05 level. [CONCLUSION]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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