Statistics Final Exam

MATH 12

FINAL EXAM

NAME:____________________________________

For all problems with an � = �. ��, �. ��, �. �� etc. 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). Please

show all of your work.

1) A researcher wishes to see if students show a time preference for anatomy labs. A

sample of four lab classes shows the enrollment. At = 0.10, do the students show a

time preference for the labs?

8AM 12PM 2PM 4PM Students 27 33 38 24

2) Four clubs were randomly selected, and quantity of their members in the clubs are

noted. At = 0.01, can it be concluded that there is a dependent relationship between

the clubs and the political party affiliation of its members?

Club 1 Club 2 Club 3 Club 4

Democrat 33 22 18 13

Republican 13 16 10 23

3) The number of annual precipitation days for one-half of the 50 largest U.S. cities is

listed below. Do the following:

131 94 136 88 116 77 127 79 47 97

116 123 88 102 27 80 156 133 117 55

112 98 55 90 125

a) Construct a frequency distribution for the data (include class boundaries in the table) with

5 classes.

b) Graph its histogram.

c) Plot its cumulative frequency (ogive).

d) Find the mode of the data.

e) Find the mean, � , for the grouped data.

f) Find the variance and standard deviation for grouped data.

g) Find the z score and percentile for the value 98.

4) The table below represents the college degrees awarded in a recent academic year by

gender.

Bachelor’s Master’s Doctorate

Men 522,733 221,412 28,400

Women 784,254 289,265 22,688

Choose a degree at random. Find the probability that it is

a) A bachelor’s degree

b) A doctorate or a degree awarded to a man

c) A doctorate awarded to a man

d) Not a master’s degree

5) The probability that Sam parks in a no-parking zone and gets a parking ticket is 0.12,

and the probability that Sam cannot find a legal parking space and has to park in the

no-parking zone is 0.17. On Tuesday, Sam arrives at school and has to park in a no-

parking zone. Find the probability that he will get a parking ticket.

6) Three cards are drawn from an ordinary deck and not replaced. Find the probability of

these events.

a) Getting 3 jacks

b) Getting an ace, a king, and a queen in order

7) Five bands and two comics are performing for a student talent show. How many

different programs (in terms of order) can be arranged? How many if the comics must

perform between bands?

8) If a person can select 5 ornaments out of 16 ornaments in a box to hang on a

Christmas tree, how many different combinations are there?

9) How many different 6-color code stripes can be made on a van if each code consists

of the colors green, red, blue, yellow, gold, and white? All colors are used only once.

10) A researcher claims that based on the information obtained from CHOC, 27% of

young people ages 3-19 are obese. To test this claim, she randomly selected 300

people ages 3-19 and found that 103 were obese. At = 0.05, is there enough

evidence to reject the claim?

11) Is there a significant difference at = 0.10 in the average heights in feet of high

towers in Europe and the ones in South Africa? The data are shown.

Europe South Africa 497 1236 1288 714 705 964

463 1312 987 1227 325 830

888 365 369 721 1799

12) A “Filler” fills 16-ounce bottles with beer. For the “Filler” to operate properly, the

standard deviation of the population must be less than or equal to 0.04. A random

sample of 10 bottles is selected, and the number of ounces of beer in each bottle

recorded. At = .01, can we reject the claim that the “Filler” is operating properly.

16.02 16.04 16.01 15.99 15.97

15.96 15.94 16.05 16.02 16.05