Question

the realtor and her clients do not know the average home sale price for all of guelph. however, they calculate that average sale price for their 10 listings is 430. given that the standard deviation of sale prices is known to be 120 , test the hypothesis that the average sale price in guelph is equal to 500. use a 1 percent. based on the hypothesis test, should we reject the null ?

Answer 1

To test the hypothesis that the average sale price in Guelph is equal to $500, we can perform a one-sample t-test using the given information.

Step-by-step explanation:

To test the hypothesis that the average sale price in Guelph is equal to $500, we can perform a one-sample t-test using the given information.

The null hypothesis is that the average sale price in Guelph is equal to $500, and the alternative hypothesis is that it is not equal to $500.

Using the formula for a one-sample t-test, we can calculate the t-value:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

For this problem, the sample mean is $430, the hypothesized mean is $500, the sample standard deviation is 120, and the sample size is 10.

Plugging in these values, we get:

t = (430 - 500) / (120 / sqrt(10)) = -2.31

Looking up the critical t-value for a one-tailed test with a 1% significance level and 9 degrees of freedom, we find that the critical t-value is approximately -2.821.

Since the calculated t-value (-2.31) is less than the critical t-value (-2.821), we can reject the null hypothesis.

Therefore, based on the hypothesis test, we should reject the null hypothesis and conclude that the average sale price in Guelph is not equal to $500.