A marketing firm asked a random set of married women and married men how much they were willing to spend for jewellery as a present for their spouse.Can the firm conclude, at , that
Each of the two groups has a different willingness to spend? (Use the unequal variances formula.)

A)No, because the test value 0.32 is inside the interval (-2.31, 2.31)
B)Yes, because the test value 2.81 is outside the interval (-2.36, 2.36)
C)Yes, because the test value 16.00 is inside the interval (-2.31, 2.31)
D)No, because the test value 16.00 is outside the interval (-2.36, 2.36)

Question

A marketing firm asked a random set of married women and married men how much they were willing to spend for jewellery as a present for their spouse.Can the firm conclude, at  , that
Each of the two groups has a different willingness to spend? (Use the unequal variances formula.)

A)No, because the test value 0.32 is inside the interval (-2.31, 2.31) 
B)Yes, because the test value 2.81 is outside the interval (-2.36, 2.36) 
C)Yes, because the test value 16.00 is inside the interval (-2.31, 2.31) 
D)No, because the test value 16.00 is outside the interval (-2.36, 2.36)

Quizplus · Accepted Answer

Based on the given information, the unequal variances formula is used to determine if there is a significant difference between the willingness to spend of the two groups. The test value is calculated to be 2.81, which is outside the interval (-2.36, 2.36) at a 5% level of significance. Therefore, the firm can conclude that there is a significant difference in the willingness to spend between the two groups. The question asks if the marketing firm can conclude that the two groups (married women and married men) have a different willingness to spend on jewellery. To answer this, we need to look at the test value and the interval. The test value is 2.81, which means that the difference in means between the two groups is 2.81 standard errors away from 0. The interval (-2.36, 2.36) represents the range of values that we would expect to see if there were no difference between the two groups (i.e., if the null hypothesis were true). Because the test value falls outside this interval, we can reject the null hypothesis and conclude that the two groups have a different willingness to spend on jewellery. Therefore, the best choice is B.

A Marketing Firm Asked a Random Set of Married Women