Question

1. Match the following situations with the correct test statistic distribution. Provide the correct test statistic you would use (or what type of test). Provide an explanation as to why this is the correct distribution or test. (2 points)

A. normal distribution

B. t distribution with 29 degrees of freedom

C. t-distribution with 70 degrees of freedom

D. Chi-square with 2 degrees of freedom

E. Chi-square with 1 degree of freedom

Match	Question Items
__ ___	A. The sponsors of televisions shows targeted at the market of 5 – 8 year olds want to test the hypothesis that children watch television at most 20 hours per week. The population of viewing hours per week is known to be normally distributed with a standard deviation of 6 hours. A market research firm conducted a random sample of 30 children in this age group. Test statistic: Explanation:
_ ___	B. A sample of 30 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1. Assume the distribution of the population is normal. Test statistic: Explanation:
______	C. A fast food restaurant is considering a promotion that will offer customers to purchase a toy featuring a cartoon movie character. If more than 20% of the customers purchase the toy, the promotion will be profitable. A sample of 30 restaurants is used to test the promotion. Test statistic: Explanation:
______	D. Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known. The sample sizes are n1 = 32 and n2 = 40. Test statistic: Explanation:
______	E. A school administrator believes that there is no difference between student dropout rate for schools located in rural areas and schools located in urban areas. A random sample of 100 schools in the rural areas was taken. The student dropout rate of the schools in the sample was 27%. A random sample of 80 schools in the urban areas had a dropout rate of 20%. Test statistic: Explanation:
______	F. In 2003, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2004, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see whether there has been a significant change in the proportions between 2003 and 2004 Test statistic: Explanation:
______	G. Dr. Sherri Brock’s diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not. Diet Pills No Diet Pills Total No Weight Loss 80 20 100 Weight Loss 100 100 200 Total 180 120 300              We want to see if losing weight is independent of taking the diet pills. Test statistic: Explanation:

Answer 1

(A)

Correct option:

Test Statistic: A.    normal distribution

Explanation: Sample Size = n = 30 Large Sample. Population Standard Deviation = = 6 is provided. So, Central Limit Theorem is applicable.

(B)

Correct option:

Test Statistic: B.    t distribution with 29 degrees of freedom

Explanation: Sample Size = n = 30 Large Sample. Population Standard Deviation = is not provided. So, t distribution with 29 degrees of freedom is applicable.

(C)

Correct option:

Test Statistic: A.   normal distribution

Explanation: Sample Size = n = 30 Large Sample. Population proportion of 0.30 is tested. So, Central Limit Theorem is applicable.

(D)

Correct option:

Test Statistic: C.   t-distribution with 70 degrees of freedom

Explanation: Sample Size = n1 = 32, n2 = 40 Large Sample. Population  Standard Deviation = is not provided. So, t distribution with degrees of freedom n1 + n2 - 2 = 32 + 40 - 2 = 70 is applicable.

(E)

Correct option:

Test Statistic:: A.   normal distribution

Explanation: Sample Size = n1 = 100, n2 = 80 Large Sample. Significance of difference in proportions is tested. So, Central Limit Theorem is applicable.

(F)

Correct option:

Test Statistic: D.    Chi-square with 2 degrees of freedom

Explanation: Chi-square Test of goodness of fit is conducted. Degrees of Freedom = 3 - 1 = 2

(G)

Correct option:

Test Statistic: D.    Chi-square with 1 degrees of freedom

Explanation: Chi-square Test of independence is conducted. Degrees of Freedom = (r - 1) X (c - 1) = (2 - 1) X (2 - 1) = 1