A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation.At is a difference in the two amounts?

A)No, because the test value 0.26 is inside the interval (-1.96, 1.96)
B)Yes, because the test value 3.81 is outside the interval (-1.96, 1.96)
C)Yes, because the test value 1.33 is inside the interval (-1.96, 1.96)
D)No, because the test value 1.33 is outside the interval (-1.96, 1.96)

Question

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation.At  is a difference in the two amounts?

A)No, because the test value 0.26 is inside the interval (-1.96, 1.96) 
B)Yes, because the test value 3.81 is outside the interval (-1.96, 1.96) 
C)Yes, because the test value 1.33 is inside the interval (-1.96, 1.96) 
D)No, because the test value 1.33 is outside the interval (-1.96, 1.96)

Quizplus · Accepted Answer

The question is asking if there is a significant difference in the amounts that married and single men are willing to spend on a vacation. This is tested using a two-sample t-test, and the test value is calculated to be 3.81. To determine if this test value is significant, we compare it to the critical values of a t-distribution with degrees of freedom equal to the sample sizes minus 2. The interval (-1.96, 1.96) represents the range of values that would not be significant at the 0.05 level. The test value of 3.81 falls outside this interval, indicating that the difference in amounts that married and single men are willing to spend is statistically significant. Therefore, choice B is correct. A difference in means test was conducted to determine if there is a significant difference between the amount that married and single men are willing to spend on vacation. The test value calculated was 3.81, which is greater than the critical value of 1.96 (for a significance level of 0.05). Therefore, we reject the null hypothesis and conclude that there is a significant difference in the amounts that married and single men are willing to spend on vacation. Thus choice B is the correct answer.

A Marketing Firm Asked a Random Set of Married and Single