MATH& 146

Lesson 31

Graphing Calculators Part 2

1

Tests and Intervals on the

Graphing Calculator

Parameter Hypothesis Test

Confidence

Interval

p 1-PropZTest 1-PropZInt

p1 – p2 2-PropZTest 2-PropZInt

μ (mu) TTest TInterval

μd TTest TInterval

μ1 – μ2 2-SampleTTest 2-SampleTInt

2

One-Proportion Z Test

For proportions, p-values and confidence intervals

can be found on a graphing calculator with the

1-PropZTest and 1-PropZInt commands:

• STAT | TESTS | 1-PropZTest (for tests)

• STAT | TESTS | 1-PropZInt (for intervals)

Enter the number of successes (x), the sample

size (n), and either the null value (p0) or the

confidence level (C-level).

3

One-Proportion Z Test

4

Hyp

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Tests

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Example 1

Suppose a random sample of size 100 had 33

successes.

a) Test the hypotheses

Use a significance level of 0.10.

b) Find the 90% confidence interval to estimate p.

Where is the null value of 0.3 on this interval?

5

0 : 0.3, : 0.3.aH p H p

Example 2

For a class project, a political science student at a

large university wants to determine the percent of

students that are registered voters. He surveys

120 students and finds that 72 are registered

voters. Compute and interpret a 90% confidence

interval for the true percent of students that are

registered voters.

6

Example 3

Duck hunting in populated areas faces opposition

on the basis of safety and environmental issues.

In a survey to assess public opinion regarding

duck hunting on Morro Bay (located along the

central coast of California), a random sample of

750 local residents included 560 who strongly

opposed hunting on the bay. Does this sample

provide convincing evidence that a majority of local

residents oppose hunting on Morro Bay?

7

Two-Proportion Z Test

For the difference of proportions, p-values and

confidence intervals can be found with the

2-PropZTest and 2-PropZInt commands:

• STAT | TESTS | 2-PropZTest (for tests)

• STAT | TESTS | 2-PropZInt (for intervals)

Enter the numbers of successes (x) and sample

sizes (n) for each group, and, for intervals, the

confidence level (C-level).

8

Two-Proportion Z Test

9

Hyp

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Example 4

The National Sleep Foundation asked a random

sample of 1010 U.S. adults questions about their

sleep habits. Split into two age categories, 26% of

the 184 people under 30 snored, compared with

39% of the 811 in the older group. Is this

difference in the proportion of snoring statistically

significant, or is it due only to natural fluctuations in

the sample we've chosen?

10

Example 5

Results on seat belt usage from the 2003 Youth Risk

Behavior Survey were published in a USA Today

Snapshot on January 13, 2005. The following table

outlines the results from the high school students who

were surveyed in the state of Nebraska. They were

asked whether or not they rarely or never wear seat

belts when riding in someone else's car. Is the

difference between females and males statistically

significant?

Female Male

Rarely or never use seat belt 208 324

Uses seat belt 1217 1184

One-Sample T Test

For means, p-values and confidence intervals can

be found on a graphing calculator with the T-Test

and TInterval commands:

• STAT | TESTS | T-Test (for tests)

• STAT | TESTS | TInterval (for intervals)

If known, choose "Stat" enter the mean and

standard deviation. Otherwise, enter your data in

the lists and choose "Data".

12

One-Sample T Test (Stats)

13

Hyp

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One-Sample T Test (Data)

14

Hyp

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Example 6

Consumer Reports tested 14 brands of vanilla yogurt

and found the following numbers of calories per

serving:

160 200 220 230 120 180 140

130 170 190 80 120 100 170

A diet guide claims that you will get 120 calories from a

serving of vanilla yogurt. What does our evidence

indicate?

15

Paired T Test

For paired means, p-values and confidence

intervals can be found on a graphing calculator

with the T-Test and TInterval commands:

• STAT | TESTS | T-Test (for tests)

• STAT | TESTS | TInterval (for intervals)

If known, choose "Stat" enter the mean and

standard deviation of the differences. Otherwise,

enter your data in the lists and choose "Data".

16

Paired T Test

Enter your two sample in L1 and L2, then use the

formula L3 = L2 – L1 to calculate the differences.

17

One-Sample T Test (Data)

18

Hyp

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Use the list

with your

differences.

Example 7

A study was conducted to

investigate the effectiveness

of hypnotism in reducing

pain. Results for randomly

selected subjects are shown

in the table, with higher

numbers indicating greater

pain. Are the results

statistically significant?

19

Subject Before After

A 6.6 6.8

B 6.5 2.4

C 9.0 7.4

D 10.3 8.5

E 11.3 8.1

F 8.1 6.1

G 6.3 3.4

H 11.6 2.0

Two-Sample T Test

For difference of means, p-values and confidence

intervals can be found on a graphing calculator

with the 2SampTTest and 2SampTInt commands:

• STAT | TESTS | 2SampTTest (for tests)

• STAT | TESTS | 2SampTInt (for intervals)

If known, choose "Stat" enter the mean and

standard deviation for the two groups. Otherwise,

enter your data in the lists and choose "Data".

20

Two-Sample T Test (Stats)

21

Hyp

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esis

Tests

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Two-Sample T Test (Data)

22

Hyp

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Pooling Variance

When using the two-sample t-test on the calculator,

you will be asked to choose whether to pool the

variance.

The Pooled t Test is the theoretically correct method

only when we have a good reason to believe the

variances of the two samples are equal. However, it's

never wrong not to pool (for at least 30 minutes after

eating). For our class, play it safe and choose "No."23

Degrees of Freedom

The calculator calculates degrees of freedom

differently than we will in class. Because of that,

p-values and confidence intervals will be slightly

different.

22 21 2

1 2

2 22 21 2

1 1 2 2

df

1 1

1 1

s s

n n

s s

n n n n

24

Example 8

A study is done by a community group in two

neighboring colleges to determine which one

graduates students with more math classes. College A

samples 110 graduates. Their average is 4.2 math

classes with a standard deviation of 1.5 math classes.

College B samples 98 graduates. Their average is 3.8

math classes with a standard deviation of 1.2 math

classes. Test to see if there is a statistical difference

between the two colleges.

25

Example 9

The data show the

sugar content (as a

percentage of weight)

of several national

brands of children's and

adults' cereals. Create

and interpret a 95%

confidence interval for

the difference in mean

sugar content.

26

Children's Adult's

40.3 20

55 30.2

45.7 2.2

43.3 7.5

50.3 4.4

45.9 22.2

53.5 16.6

43 14.5

44.2 21.4

44 3.3

Goodness of Fit Test

For testing many proportions, conduct a Goodness

of Fit Test with the χ2GOF-Test command (TI-84

only):

• STAT | TESTS | χ2GOF-Test

Before using the test, enter the Observed values in

L1 and Expected values in L2. Remember that the

degrees of freedom is k – 1.

27

Goodness of Fit Test

28

Hyp

oth

esis

Tests

Example 10

The Masterfoods Company says that until recently

yellow candies made up 20% of its milk chocolate

M&M's, red another 20%, and orange, blue, and

green 10% each. The rest are brown. On his way

home from work, Mark bought a bag of plain

M&M's. He got 29 yellow ones, 23 red, 12 orange,

14 blue, 8 green, and 20 brown. Is this sample

consistent with the company’s stated proportions?

Test an appropriate hypothesis and state your

conclusion.

Test for Independence

For testing many proportions, conduct a Goodness

of Fit Test with the χ2GOF-Test command (TI-84

only):

• STAT | TESTS | χ2GOF-Test

Before using the test, enter the Observed values in

L1 and Expected values in L2. Remember that the

degrees of freedom is k – 1.

30

Creating a Matrix

For this test, you must first enter your contingency

table in Matrix [A], then create a matrix of the

same size in Matrix [B].

2ND MATRIX

EDIT 1: [A], then enter your contingency table

EDIT 2: [B], have dimensions match [A], but you

don't need to enter any expected values.

Test for Independence

32

En

ter

Data

Hyp

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Test

Example 11

Suppose that we want to poll registered voters about a

piece of legislation proposed by the governor. In the

poll, 200 urban, 200 suburban, and 100 rural residents

are randomly selected and asked whether they favor

or oppose the governor's proposal.

Residence Favor Oppose Total

Urban 143 57 200

Suburban 98 102 200

Rural 13 87 100

Total 254 246 500

Example 11 continued

That is, a simple random sample is taken for each of

these three groups. Is there sufficient evidence to

reject the hypothesis that the proportion of those who

favor the proposal is the same for all three groups?

Residence Favor Oppose Total

Urban 143 57 200

Suburban 98 102 200

Rural 13 87 100

Total 254 246 500