Question

Question 6 1.25 pts The Department of Housing and Urban Development (HUD) would like to test the hypothesis that the average size of a newly constructed house last year is different from the average size of a newly constructed house in 2000. The following data summarizes the sample statistics for house sizes, in square feet, for both years. Assume that the population variances are known. 2000 Last Year 2,290 2,460 Sample mean Sample size Population standard deviation 18 18 250 260 If Population 1 is defined as homes built in 2000 and Population 2 is defined as homes built last year, and using a = 0.10, the conclusion for this hypothesis test would be that because the absolute value of the test statistic is less than the absolute value of the critical value, HUD cannot conclude that the average size of a newly constructed house last year is different from the average size of a newly constructed house in 2000 less than the absolute value of the critical value, HUD can conclude that the average size of a newly constructed house last year is different from the average size of a newly constructed house in 2000 more than the absolute value of the critical value, HUD can conclude that the average size of a newly constructed house last year is different from the average size of a newly constructed house in 2000 more than the absolute value of the critical value, HUD cannot conclude that the average size of a newly constructed house last year is different from the average size of a newly constructed house in 2000 O none of these answers are correct

Answer 1

The data of the HUD is given below: .*; Sample mean of population 1 = 2,290 X2, Sample mean of population 2 = 2,460 0, Population 1 standard deviation = 250 02, Population 2 standard deviation = 260 n, Sample size of population 1 = 18 ny, Sample size of population 2 = 18 Consider the Null hypothesis and Alternative hypothesis as shown below: There is no difference between the average size of the houses constructed in the year 2000 and in the last year H: Null Hypothesis Un = uz There is a difference between the average size of the houses constructed in the year 2000 and in the last year H : Alternative Hypothesis My F M Calculate the t-test using the following formula:

t observed 1 1 + X – , (( -1)xơ)+((n, -1)xơ). n + n - 2 2,290 -2,460 ((18-1)x(250))+((18-1) (260)") n n 1 18+18-2 18 18 -170 1,062,500 +1,149,200 34 9 -170 2,211,700 306 -170 85.0163 =-1.9996 I critical = t. 9.07 =10.10 1970 n 183-2 = 10.05.(18+18–2) = 10.0534 a From the t-statistical table, find the value of t where df = 34 and = 0.05 2

taitical = -1.6909 observed Therefore, from the above calculation, t critical served · There is no strong evidence to reject the null hypothesis. Hence, one can conclude that there is no difference between the average size of the houses constructed in the year 2000 and in the last year. Therefore, the correct option is less than the absolute value of the critical value, HUD cannot conclude that the average size of a newly constructed house last year is different from the average size of a newly constructed house in 2000.