MATH&146

Exam 3 Review

Lessons 24 – 34

1

Parameter Hypothesis Test

p One-Proportion Z Test

p1 – p2 Two-Proportion Z Test

p1, p2, …, pk Chi-Square Tests

μ (mu) One-Sample T Test

μd Paired T Test

μ1 – μ2 Two-Sample T Test

μ1 = μ2 = … = μk ANOVA Test

Hypothesis Tests (so far)

2

Exam

3

Example 1

Last year's work record for absenteeism in each of four

categories from 500 randomly selected employees is

compiled in the following table. Do these data provide

sufficient evidence to reject the hypothesis that the

rate of absenteeism is the same for all categories of

employees?

3

Married

Male

Single

Male

Married

Female

Single

Female

Percent of Employees 40% 14% 16% 30%

Days Absent (Observed) 180 110 75 135

Days Absent (Expected) 40% of 500

= 200

14% of 500

= 70

16% of 500

= 80

30% of 500

= 150

Example 2

The manager of an assembly process wants to

determine whether or not the number of defective

articles manufactured depends on the day of the week

the articles are produced the following information.

a) Identify the expected count for the number of

defective articles on Wednesday.

4

Day of Week M Tu W Th F Total

Nondefective 85 90 95 95 90 455

Defective 15 10 5 5 10 45

Total 100 100 100 100 100 500

Example 2 continued

b) What are the degrees of freedom for this test?

c) For the test statistic χ2 = 8.547, compute the p-

value.

d) What is the conclusion of the test?

5

Day of Week M Tu W Th F Total

Nondefective 85 90 95 95 90 455

Defective 15 10 5 5 10 45

Total 100 100 100 100 100 500

Example 3

Use the given information to calculate and interpret the

test statistic and effect size.

Hypotheses: H0: μ = 20 vs. Ha: μ ≠ 20

Sample data

= 19.8

SD = 1.5

SE = 0.25

x

6

Example 4

Waiters are expected to keep track of their income

from tips and report it on their income tax forms. The

Internal Revenue Service suspects that one waiter

(we'll call him "Fred") has been under-reporting his

income, so they are auditing his tax return.

An IRS agent goes through the restaurant's files and

obtains a random sample of 80 credit card receipts

from people Fred served. The average tip size shown

on these receipts was $9.68 with a standard deviation

of $2.72.

7

Example 4 continued

a) Create a 90% confidence interval for Fred's

average credit card tips.

b) On his tax return Fred had claimed that his tips

averaged $8.73. Based on their confidence

interval, does the IRS have a case against him?

Explain.

8

Example 5

At the end of their first day at

training camp, 10 new

recruits participated in a rifle-

shooting competition. The

same 10 competed again at

the end of a full week of

training and practice. Their

results are shown in the

following table.

9

Recruit

First

day

One week

later Diff

1 72 75 3

2 29 43 14

3 62 63 1

4 60 63 3

5 68 61 –7

6 59 72 13

7 61 73 12

8 73 82 9

9 38 47 9

10 48 43 –5

diff = one week later – first day

Example 5 continued

Does this set of 10 pairs of

data show that there is a

significant amount of

improvement in the recruits'

shooting abilities during the

week?

10

Recruit

First

day

One week

later Diff

1 72 75 3

2 29 43 14

3 62 63 1

4 60 63 3

5 68 61 –7

6 59 72 13

7 61 73 12

8 73 82 9

9 38 47 9

10 48 43 –5

diff = one week later – first day

Example 6

An agronomist hopes that a new fertilizer she has

developed will enable grape growers to increase the

yield of each grapevine. To test this fertilizer she

applied it to 44 vines and used the traditional growing

strategies on 47 other vines. The fertilized vines

produced a mean of 58.4 pounds of grapes with

standard deviation 3.7 pounds, while the unfertilized

vines yielded a mean of 52.1 pounds with standard

deviation 3.4 pounds of grapes. Do these

experimental results confirm the agronomist's

expectations?

11

Example 6 continued

Find and interpret the effect size. Use 3.55 for the

standard deviation of the differences in students'

attitudes.

12

Sample size Mean St Dev

Fertilized vines 44 58.4 3.7

Unfertilized vines 47 52.1 3.4

2 21 1 2 2

1 2

1 1Note:

2

n s n sSD

n n

Example 7

Complete the missing values in the following ANOVA

table.

13

DF SS MS F Pr(>F)

Group 2

Error 156.7

Total 197 158.0

Example 8

An employment agency wants to see which of three

types of ads in the help-wanted section of local

newspapers is the most effective. Three types of ads

(big headline, straightforward, and bold print) were

randomly alternated over a period of weeks, and the

number of people responding to the ads was noted

each week (next slide). Do these data support the null

hypothesis that there is no difference in the

effectiveness of the ads, as measured by the mean

number responding?

14

Example 8 continued

Big Headline Straightforward Bold Print

23 19 28

42 31 33

36 18 46

48 24 29

33 26 34

26 34

15

DF SS MS F Pr(>F)

Type of Ad

Error

Total