Question

Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester.

University A University B
Sample Size 50 40
Average Purchase $280 $250
Standard Deviation $20 $23
At 95% confidence test to determine if, on the average, students at University A spend more on textbooks then the students at University B.

Answer 1

Z > Zα

6.511 > 1.645

Explanation:

University A University B

Sample Size 50 40

Average Purchase $280 $250

Standard Deviation $20 $23

We formulate

H0: x1` > x2` null hypothesis that the mean of the University A is greater than the mean of the University B

HA: x1`≤ x2` one tailed test

Test statistic

Z= x1`-x2`/ √s₁²/n₁ +s²₂/n₂

Z= 280-250/√400/50 + 529/40

Z= 30/√8 +13.225

Z= 30 /4.607

Z= 6.511

For one tailed test at α= 0.05 = 1.645

Z > Zα

6.511 > 1.645

Thus we reject null hypothesis.On the average, students at University A spend more on textbooks then the students at University B.