Question

Consider the housing market.
Researchers are attempting to discover the average change in the price of homes in
the Twin Cities, for November 2019.
They have sampled 256 homes, and found the following sample statistics:
Mean Change = 1.06 %
Standard Deviation = .8 %
Using a level of significance equal to .05, test the null hypothesis that
the true population mean is equal to 1.00 % against the alternative
hypothesis that it is not equal to 1.00 % ( show your work).

Answer 1

The hypotheses are :

H0 : The mean change in price homes is equal to 1.00% , i.e , = 1.00

H1 : The mean change in price homes is not equal to 1.00% , i.e , 1.00

Here, n = 256 , = 1.06 and s = 0.8

alpha = 0.05

The test statistic , t = ( - ) / (s / n)

= 0.06 / 0.05

= 1.2

Degrees of freedom = n -1

= 255

Now, at alpha = 0.1 and df = 255 , we find the critical value of t from the critical values table.

t(critical) = 1.97

Therefore , t < t(critical) and hence, we fail to reject the null hypothesis at alpha = 0.1.

We conclude that the population mean change in price homes is equal to 1.00%.