Question

1. Determine if the following situations are either

• One Sample Mean
• One Sample Proportion
• Two Independent Sample Means
• Two Independent Sample Means Pooled t-Test
• Levene’s Test
• Paired Data t-Test
• Two Independent Sample Proportions
• Goodness of Fit Test

a) A high school principal claims that 30% of student athletes drive themselves to school, while 4% of non-athletes drive themselves to school. In a sample of 20 student athletes, 45% drive themselves to school. In a sample of 35 non-athlete students, 6% drive themselves to school. Is the percent of student athletes who drive themselves to school more than the percent of nonathletes?

b) A sample of 12 in-state graduate school programs at school A has a mean tuition of $64,000 with a standard deviation of $8,000. At school B, a sample of 16 in-state graduate programs has a mean of $80,000 with a standard deviation of $6,000. On average, are the mean tuitions different? Assume the variance of both schools are the same.

c) A study of sterility in the fruit fly (“Hybrid Dysgenesis in Drosophila melanogaster: The Biology of Female and Male Sterility,” Genetics, 1979: 161–174) reports the following data on the number of ovaries developed by each female fly in a sample of size 1388. One model for unilateral sterility states that each ovary develops with a probability of 1/3 independently of the other ovary.

Number of Ovaries	0	1	2
Observed Count	1212	118	58

d) One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal.

e) At Rachel’s 21th birthday party, 16 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The sample mean and variance of the difference between their jumping and relaxed times is -3.2 (Jumping minus relaxed) and 9.2342 .The girls thought that the mean difference between their jumping and relaxed times would be zero.

Answer 1

Part a :

Given are two samples of athletes and non athletes on whether they drive to school or not and the problem statement is to determine each groups population, Considering that the two events are independent of each other, the appropriate test to use

Two Independent Sample Proportions Test

Part b :

This is a test of variance, where we are provided with 2 samples with different size and means. Hence the appropriate test would be,

Levene's Test

Part c :

Given, is a model based on observations on the sample size of 1388, the frequency distribution is provided. The correct test would be,

Goodness of Fit test

Part d

Given is a single sample of 108 Americans to determine the average hours spent by them in watching tv. Appropriate testing approach would be,

One sample mean

Part e

We have observations on 2 variables, based on the same target and the objective is to test for the difference in means, with the idea that the mean difference is 0. Correct approach of testing is,

Paired Data T test