Question

Question 3 Experience has shown that Male applicants to Virginia Tech score on average 3.5 points better on the science placement than Female applicants. Following a random sample of these years freshman applications for admission resulted in the data below: Gender Males Females Sample Size 25 35 Mean Score 71.5 71.2 Standard deviation 10.3 11.2 A) Is there sufficient evidence that males score significantly better at the alpha-0.05 level. (10 points) For the next four questions state which inference procedure you would use. Be specific. For example, you might say two-sample z test for the difference between two proportions. YOU DO NOT need to carry out any procedures, just name the test. 5. How do young adults look back on adolescent romance? Investigators interviewed 40 couples in their mid- twenties. The female and male partners were interviewed separately. Each was asked about his or her current relationship and also about a romantic relationship that lasted at least two months when they were aged 15 or 165. One response variable was a measure on a numerical scale of how much the attractiveness of the adolescent partner mattered. You want to find out how much men and women differ on this measure 6. Are more than 75% of Toyota owners generally satisfied with their vehicles? Les design a study to find out. We will select a random sample of 400 Toyota owners. Then we'll ask each individual in the sample: "Would you say that you are generally satisfied with your Toyota vehicle?" 7. Are male college students more likely to binge drink than female college students? The Harvard School of Public Health surveys random samples of males and female undergraduates at four year colleges and universities about they have engaged in binge drinking. 8. A bank wants to know which of two incentive plans will most increase the use of its credit cards and by how much. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months.

Answer 1

n1 = 25, n2 = 35, x1-bar = 71.5, x2-bar = 71.2, s1 = 10.3, s2 = 11.2    

Ho: μ1 ≤ μ2    

Ha: μ1 > μ2    

α = 0.05    

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = √(((25 - 1) * 10.3^2 + (35 - 1) * 11.2^2)/(25 + 35 - 2)) = 10.8367

SE = s * √{(1 /n1) + (1 /n2)} = 10.8367 * √((1/25) + (1/35)) = 2.838

t = (x1-bar -x2-bar)/SE = (71.5 - 71.2)/2.838 = 0.1057

p- value = 0.4581   

Since 0.4581 > 0.05, we fail to reject Ho

There is no enough statistical evidence that males score significantly better than females.