Penn State STAT 200 Assignment

# 1. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.

c. If the problem is a hypothesis test, indicated if it has a lower-tail, upper-tail, or two-tail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.

Unless indicated otherwise, you DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc. Just type your answer to a., b., and c. above in the space below.

Problem: A large organization is being investigated to determine if its recruitment is sex-biased. Tables 1 and 2, respectively, show the classification of applicants for sales and for secretarial positions according to gender and result of interview. Table 3 is an aggregation of the corresponding entries of Table 1 and Table 2. Answer each of the following:

i. According to the data in tables 1 and 2, does there seem to be an association with gender and hiring status at the 5% significance level?

ii. Does the data in Table 3 indicate the same result?

Table 1 Sales Positions

	Offered	Denied	Total
Male	25	50	75
Female	75	150	225
Total	100	200	300

Table 2 Secretarial Positions

Offered

Denied

Total

Male

150

200

Female

100

Total

225

300

Table 3 Secretarial and Sales Positions

Offered

Denied

Total

Male

175

100

275

Female

150

175

325

Total

325

275

600

# 2. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.

Problem: An instructor at Arizona State University asked a random sample of 8 students to record their study times in a elementary statistics course. She then made a table for total hours studied over 2 weeks and test scores at the end of the 2 weeks. Here are the data:

Study time 10 15 12 20 8 16 14 22

Test Scores 92 75 86 76 92 80 84 81

Assuming that a linear association exists, how are the data correlated? Determine the exact linear relationship between study time and test scores and use it to estimate the predicted test score for a student who studies 12 hours.

# 3. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.

Problem: A company sells a strong commercial floor cleaner and claims that the flashpoint (the lowest temperature at which the vapor of a combustible liquid can be ignited in air) exceeds 200ºF. A random sample of cleaner was obtained and the flashpoint of each was measured. The sample mean was 198.2ºF and the sample standard deviation was 10ºF. At the 1% significance level, is there sufficient evidence to support the companies claim?

# 4. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.

Summary Table for Statistical Techniques

Inference

Parameter

Statistic

Type of

Data

Examples

Analysis

Minitab

Command

Conditions

Estimating a

mean

One

population

mean µ

sample mean

numerical

What is the average

weight of adults?

What is the average

cholesterol level of

adult females?

1-sample t-interval

Stat

>Basic

statistics

>1-sample t

data approximately normal

have a large sample

size (n ≥ 30)

Test about a

mean

One

population

mean µ

sample mean

numerical

Is the average GPA

of juniors at Penn

State higher than

3.0?

Is the average

Winter temperature

in State College

less than 42ْ F?

H_o: µ = µ_o

H_a: µ ¹ µ_oor H_a: µ > µ_o

or H_a: µ < µ_o

The one sample t test:

Stat

>Basic

statistics

>1-sample t

data approximately normal

have a large sample

size (n ≥ 30)

Estimating a

proportion

One

population

proportion

sample

proportion

categorical

(binary)

What is the

proportion of males

in the world?

What is the

proportion of

students that smoke?

1-proportion Z-interval

Stat

>Basic

statistics

>1-sample

proportion

n≥ 10 and n (1-) ≥ 10

Test about a

proportion

One

population

proportion

sample

proportion

categorical

(binary)

Is the proportion

of females different

from 0.5?

Is the proportion of

students who fail

Stat200 less than

0.1?

H_o: p = p_o

H_a: p ¹ p_oor H_a: p > p_o

or H_a: p < p_o

The one proportion Z-test:

Stat

>Basic

statistics

>1-sample

proportion

n p_o³ 10andn (1-p_o) ³ 10

Inference

Parameter

Statistic

Type of

Data

Examples

Analysis

Minitab

Command

Conditions

Estimating the

difference of

two means

difference in

two

population

means

µ₁-µ₂

difference in

two sample

means

numerical

How different are

the mean GPAs of

males and females?

How many fewer

colds do vitamin C

takers get, on

average, than non

vitamin C takers?

two-sample t-interval

See text, page 445, for

the s.e. of the difference

Stat

>Basic

statistics

>2-sample t

independent samples from

the two populations

data in each sample are

about normal or large

samples (n_i ≥ 30)

Test to

compare two

means

difference in

two

population

means

µ₁-µ₂

difference in

two sample

means

numerical

Do the mean pulse

rates of exercisers

and non-exercisers

differ?

Is the mean EDS

score for dropouts

greater than the

mean EDS score for

graduates?

H_o: µ₁ = µ₂

H_a: µ₁ ¹ µ₂or H_a: µ₁ > µ₂

or H_a: µ₁ < µ₂

The two sample t test:

See text, page 445, for

the s.e. of the difference

Stat

>Basic

statistics

>2-sample t

independent samples from

the two populations

data in each sample are

about normal or large

samples (n_i ≥ 30)

Estimating a

mean with

paired data

mean of

paired

difference

µ_D

sample mean

difference

numerical

What is the

difference

in pulse rates, on the

average, before and

after exercise?

paired t-interval

Stat

>Basic

statistics

>Paired t

differences approximately

normal

have a large number

of pairs (n ≥ 30)

Test about a

mean with

paired data

mean of

paired

difference

µ_D

sample mean

difference

numerical

Is the difference in

IQ of pairs of twins

zero?

Are the pulse rates

of people higher

after exercise?

H_o: µ_D = 0

H_a: µ_D ¹ 0or H_a: µ_D > 0

or H_a: µ_D < 0

Stat

>Basic

statistics

>Paired t

differences approximately

normal

have a large number

of pairs (n ≥ 30)

Inference

Parameter

Statistic

Type of

Data

Examples

Analysis

Minitab

Command

Conditions

Estimating the

difference of

two

proportions

difference in

two

population

proportions

p₁-p₂

difference in

two sample

proportions

categorical

(binary)

How different are

the percentages of

male and female

smokers?

How different are

the percentages of

upper- and lower-

class binge

drinkers?

two-proportions Z-interval

See notes for s.e. formula

Stat

>Basic

statistics

>2 proportions

independent samples

from the two populations

n≥ 10 and (1-n)≥ 10

for each sample

Test to

compare two

proportions

difference in

two

population

proportions

p₁-p₂

difference in

two sample

proportions

categorical

(binary)

Is the percentage of

males with lung

cancer higher

than the percentage

of females with lung

cancer?

Are the percentages

of upper- and lower-

class binge drinkers

different?

H_o: p₁ = p₂

H_a: p₁ ¹ p₂or H_a: p₁ > p₂

or H_a: p₁ < p₂

The two proportion z test:

See notes for s.e. formula

Stat

>Basic

statistics

>2 proportions

independent samples

from the two populations

n≥ 10 and (1-n)≥ 10

for each sample

Relationship

in a 2-way

table

relationship

between two

categorical

variables

difference in

two or more

population

proportions

the observed

counts in a

two-way table

categorical

Is there a

relationship

between smoking

and lung cancer?

Do the proportions

of students in each

class who smoke

differ?

H_o: The two variables are

not related

H_a: The two variables are

The chi-square statistic:

Stat

>Tables

>CrossTabu-

lation >Chi-

Square analysis for

For summarized

Data: Stat>

Tables> Chi-

Square.

all expected counts should

be greater than 1

at least 80% of the cells

should have an expected

count greater than 5

Inference

Parameter

Statistic

Type of

Data

Examples

Analysis

Minitab

Command

Conditions

Test about a

slope

slope of the

population

regression

line b₁

sample

estimate of

the slope

b₁

numerical

Is there a linear

relationship between

height and weight of

a person?

H_o: b₁= 0

H_a: b₁ ¹ 0or H_a: b₁ > 0

or H_a: b₁ < 0

The t test with n-2 degrees of

freedom:

Stat

>Regression

the form of the equation

that links the two variables

must be correct

the error terms are normally

distributed

the errors terms have

equal variances

the error terms are

independent of each other

Test to

compare

several

means

Population

means of the

k populations

µ_1,µ_{2,….., ,}µ_k

Sample means

of the k

populations

x_1,x_{2,….., ,}x_k

numerical

Is there a difference

between the mean

GPA of Freshman,

Sophomore, Junior

and Senior classes?

H_o: µ₁₌µ₂₌_˙˙˙₌µ_k

H_a: not all the means are

equal

The F test for one-way

ANOVA:

Stat

>ANOVA

>Oneway

each population is normally

distributed

independent samples from

the k populations

equal population standard

deviations

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