If a random sample of 21 homes south of Center Street in Provo has a mean sellin

Question

If a random sample of 21 homes south of Center Street in Provo has a mean selling price of $145,400 and a standard deviation of $4500, and a random sample of 30 homes north of Center Street has a mean selling price of $148,525 and a standard deviation of $5800, 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.

Reject the null hypothesis, there is not significant evidence of a difference in means.Reject the null hypothesis, there is significant evidence of a difference in means.    Fail to reject the null hypothesis, there is significant evidence of a difference in means.Fail to reject the null hypothesis, there is not significant evidence of a difference in means

Explanation / Answer

For independnet groups,

SE(x1bar-x2bar)=sqrt [s1^2/n1+s2^2/n2], where x1bar, x2bar correspond to mean selling price of house at south of Center strret and North of center street, s1 and s2 are corresponding sample standard deviations and n1 and n2 are th ecorresponding sample sizes.

=sqrt[4500^2/21+5800^2/30]

=1444.17

t=(x1bar-x2bar)-0/SE(x1bar-x2bar)=(145400-148525)/1444.17=-2.16

At df=48, p value is 0.035.

p value is less than alpha=0.05, reject null hypothesis, there i ssignificant evidence of difference in means.

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