Statistics Exam

MATH 12

EXAM #4

NAME:____________________________________

For problems 1, 2, and 4 provide the following:

State the hypotheses and identify the claim, find the critical value(s), compute the test

value, make the decision, summarize the results (make the appropriate statement of the

results of the claim included rejection or non-rejection of the null hypothesis).

1) Students were given an exam prior to attending a conference on anatomy. Once the

conference was completed the students were given another exam. Is there enough

evidence that the scores improved? Use � = 0.01.

Student | 1 2 3 4 5 6

Scores prior | 61 52 44 50 70 55

Scores after | 73 60 59 55 73 60

2) The average weight (23.5kg) and the average height (127.7cm) for both boys and

girls at age 10 are exactly the same. A random sample of ten year old kids yielded

these results. At � = 0.10, do the data support the given claim that there is a

difference in weights?

Boys Girls

Sample size 61 58

Mean weight, kg 20.5 26.2

Sample variance 9 11

3) A random sample of high temperatures in June and July is listed. At � = 0.05, can it

be concluded that there is a difference in variances in high temperature between the

two months?

June |110 111 122 115 106 100 117 111 103 116

July |120 115 118 124 115 98 113 101 105

For the following problem:

Draw the scatter plot for the variables, compute the value of the correlation coefficient,

state the hypotheses, identify the claim, find the critical value(s), compute the test value,

make the decision, summarize the results (make the appropriate statement of the results

of the claim included rejection or non-rejection of the null hypothesis).

4) Is there a relationship between the life expectancy for men (X) and the life

expectancy for women (Y) in a given country? A random sample of non-

industrialized countries was selected, and the life expectancy in years is listed for

both men and women. At � = 0.05, are the variables linearly related? If the solution

has a strong linear relationship, find the best fit line and graph it on the scatter plot. In

addition, find a women’s life expectancy in a country where men’s life expectancy =

70 years.

Men | 88 68 80 57 60 75

Women | 85 74 88 65 55 76