Question

A sample of 150 homes for sale in ABC City showed a mean asking price of $233,000, but the city claimed that the mean asking price for the population was $255,000. The population standard deviation of all homes for sale was $11,000. Use the p-value approach to conduct a full hypothesis test (all steps) that can be used to determine whether the mean asking price is significantly less than $255,000. Let α = .10.

Answer 1

Solution:

Given:

Sample size = n = 150

Sample mean =

The population standard deviation =

We have to test whether the mean asking price is significantly less than $255,000.

Level of significance = α = 0.10.

Step 1) State H0 and H1:

Vs

This is left tailed test, since H1 is < type.

Step 2) Test statistic

Step 3) Find p-value :

For left tailed test , p-value is:

p-value = P(Z < z test statistic)

p-value = P(Z < -24.49)

Use excel command to find above probability:

=NORM.S.DIST(z,cumulative)

=NORM.S.DIST(-24.49,TRUE)

=0.0000

Thus

p-value = 0.0000

Step 4) Decision Rule:
Reject null hypothesis H0, if P-value < 0.10 level of significance, otherwise we fail to reject H0

Since p-value = 0.0000 < 0.10 level of significance, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.10 significance level, we have sufficient evidence to reject the city's claim that  the mean asking price for the population was $255,000 and thus we conclude that:  the mean asking price is significantly less than $255,000.