Question

Suppose a real estate agent is interested in comparing the asking prices of mid-range homes in Brisbane and Canberra. The real estate agent conducts a small telephone survey in the two cities, asking the prices of mid-range homes. A random sample of 21 listings in Brisbane resulted in a sample average price of $507,600, with a standard deviation of 9,200. A random sample of 26 listings in Canberra resulted in a sample average price of $496,000, with a standard deviation of 7,000. The estate agent assumes prices of mid- range homes are normally distributed and the variance in prices in the two cities are about the same. Test whether there is any difference in the mean prices of mid-ranged homes of the two cities for α = 0.05.

B for Brisbane and C for Canberra

1. H_o: mu_B - mu_C(= ; <= ; >=)   0

H_a: mu_B - mu_C (< > ; > ; <)   0

2. Statistical test: (z / t)   test

3. Level of significance (be careful as to one-tailed or two-tailed)

4. Set up critical values (Write the value in the box, include "-" sign if negative, if two values, just write the positive one)

5. Gather sample data: xbar_B = 507,600 ; n_B = 21; (sigmaB or sB)    = 9,200; xbar_C = 496,000 ; n_C =  ; s_C = 7,000

6. Calculate test statistic (write your answer correct to 2 decimal places)  

7. Make statistical conclusion: (Reject / Do not reject)   the null hypothesis. There is (sufficient/insufficient)   evidence that there is a difference in the mean prices of mid-ranged homes of the two cities.

Answer 1