Chapter 11 Practice

A well-known surfboard company wants to determine if any of its four surfboard design types are more popular than the others. A random sample of 60 surfboards sold were identified and their design types were identified. Here are the results:

Design

Type 1: 18

Type 2: 12

Type 3: 9

Type 4: 21

Which of the following would be an appropriate null hypothesis for the company to test?

A. The observed counts are all equal to 15.

B. Surfboard design type amounts are evenly distributed across the 4 types.

C. At least one of the four types amount is different from the other three.

D. The observed count is equal to the expected counts.

E. µ1 = µ2 = µ3 = µ4

B.

This is a chi-square GOF test: one sample and one variable

So the null hypothesis should refer to the distribution of the population, not observed values.

Also, E is wrong because of "µ" being used. If those were all "p"'s instead, then it would work as well.

A well-known surfboard company wants to determine if any of its four surfboard design types are more popular than the others. A random sample of 60 surfboards sold were identified and their design types were identified. Here are the results:

Design

Type 1: 18

Type 2: 12

Type 3: 9

Type 4: 21

Which of the following are conditions that must be met in order to test this hypothesis using a chi-square test?

I. If p = proportion of surfboards sold in the population, then np≥10 and n(1-p)≥10.

II. Individual observations are independent.

III. All expected counts are greater than 5.

IV. The data must come from a random sample.

A. I and II only

B. II and III only

C. I, II, and III only

D. II, III, and IV only

E. all the above

D.

Rememer, there are 3 conditions for a chi-square test.

1.) Random - IV

2.) Large sample size - III

3.) Independent - II

A. doesn't work because we are working with a chi-square distribution, which is not Normally distributed. A. would be to test for Normality.

A well-known surfboard company wants to determine if any of its four surfboard design types are more popular than the others. A random sample of 60 surfboards sold were identified and their design types were identified. Here are the results:

Design

Type 1: 18

Type 2: 12

Type 3: 9

Type 4: 21

Which of the following represents the component of the chi-square statistic for the Type 2 design surfboard?

A. 12

B. 15

C. √((12 - 15)²/15)

D. (12 - 15 )²/15

E. (15 - 12)²/12

D.

Remember, the formula is:

(observed - expected)²/expected

A well-known surfboard company wants to determine if any of its four surfboard design types are more popular than the others. A random sample of 60 surfboards sold were identiifed and their design types were identified. Here are the results:

Design

Type 1: 18

Type 2: 12

Type 3: 9

Type 4: 21

Which of the following is a condition that must be met in order to carry out a chi-square goodness-of-fit test?

A. All observed cell counts must be greater than 5.

B. All expected cell counts must be greater than 5.

C. The cell counts for our sample have to be about the same as the expected counts.

D. The population must be normally distributed, or the sample size must be greater then 30.

E. More than one of these conditions must be met.

B.

This one satisfies the "large sample size" condition.

A well-known surfboard company wants to determine if any of its four surfboard design types are more popular than the others. A random sample of 60 surfboards sold were identiifed and their design types were identified. Here are the results:

Design

Type 1: 18

Type 2: 12

Type 3: 9

Type 4: 21

Which of the following is the correct test statistic?

A. Chi² = 6

B. Chi² = 7

C. Chi² = 8

D. Chi² = 9

E. Not enough information to determine.

A.

Remember enter in the observed counts into L1 and the expected counts into L2 and do the chi²GOF - Test in your calculator.

df = 4 - 1 =3

A well-known surfboard company wants to determine if any of its four surfboard design types are more popular than the others. A random sample of 60 surfboards sold were identiifed and their design types were identified. Here are the results:

Design

Type 1: 18

Type 2: 12

Type 3: 9

Type 4: 21

Which of the following intervals contains the P-value for this test?

A. 0.005 ≤ P-value ≤ 0.01

B. 0.01 ≤ P-value ≤ 0.025

C. 0.025 ≤ P-value ≤ 0.05

D. 0.05 ≤ P-value ≤0.1

E. P-value ≥ 0.1

E.

The P-value is 0.1116

Remember enter in the observed counts into L1 and the expected counts into L2 and do the chi²GOF - Test in your calculator.

df = 4 - 1 =3

The chi-square statistic for a particular test with 8 degrees of freedom is chi² = 20.022. Which of the following is the correct conclusion to draw?

A. Reject Ho at both α = 0.05 and α = 0.01.

B. Fail to reject Ho at both α = 0.01 and α = 0.05.

C. Reject Ho at α = 0.05; fail to reject Ho at α = 0.01.

D. Reject Ho at α = 0.01; fail to reject Ho at α = 0.05.

E. Reject Ho at α = 0.05; accept Ha at α = 0.01.

C.

The P-value is 0.0103.

Therefore, it is smaller than 0.05 and larger than 0.01. Reject at 0.05 and fail to reject at 0.01.

Do male and female toddlers show a preference for certain colors? Researchers offer identical toys of

four different colors to separate randomly selected samples of male and female children aged 15 to 20

months and record which color toy is picked up first. Here are their results:

Color of first toy chosen

--------Female:-------Male:--Total:

Red:------48----------55----103

Blue:----- 24----------34-----58

Yellow:--- 18-----------9-----27

Green:----30----------18-----48

Total:----120-------- 116----236

Under the assumption that the null hypothesis is true, which of the following represents the expected count for male children who choose a blue toy?

A. (58)(116)/34

B. (34)(58)/236

C. (34)(116)/236

D. (58)(116)/174

E. (58)(116)/236

E.

Remember, the formula to use is

(Row total)(Column total)/(Total total)

Do male and female toddlers show a preference for certain colors? Researchers offer identical toys of

four different colors to separate randomly selected samples of male and female children aged 15 to 20

months and record which color toy is picked up first. Here are their results:

Color of first toy chosen

--------Female:-------Male:--Total:

Red:------48----------55----103

Blue:----- 24----------34-----58

Yellow:--- 18-----------9-----27

Green:----30----------18-----48

Total:----120-------- 116----236

Which of the following are the degrees of freedom for the distribution of the test statistic in this situation?

A. 10

B. 8

C. 4

D. 3

E. 2

D.

Degrees of freedom = (row -1)(column - 1)

= (4 - 1)(2 - 1)

= 3

Do male and female toddlers show a preference for certain colors? Researchers offer identical toys of

four different colors to separate randomly selected samples of male and female children aged 15 to 20

months and record which color toy is picked up first. Here are their results:

Color of first toy chosen

--------Female:-------Male:--Total:

Red:------48----------55----103

Blue:----- 24----------34-----58

Yellow:--- 18-----------9-----27

Green:----30----------18-----48

Total:----120-------- 116----236

What is the test statistic in this situation?

The chi² = 8.13

Remember to create a matrix (4 x 2) for this data.

Then go to chi²-Test.

Do male and female toddlers show a preference for certain colors? Researchers offer identical toys of

four different colors to separate randomly selected samples of male and female children aged 15 to 20

months and record which color toy is picked up first. Here are their results:

Color of first toy chosen

--------Female:-------Male:--Total:

Red:------48----------55----103

Blue:----- 24----------34-----58

Yellow:--- 18-----------9-----27

Green:----30----------18-----48

Total:----120-------- 116----236

What is the P-value in this situation?

The P-value = 0.0433

Remember to create a matrix (4 x 2) for this data.

Then go to chi²-Test.

Do male and female toddlers show a preference for certain colors? Researchers offer identical toys of

four different colors to separate randomly selected samples of male and female children aged 15 to 20

months and record which color toy is picked up first. Here are their results:

Color of first toy chosen

--------Female:-------Male:--Total:

Red:------48----------55----103

Blue:----- 24----------34-----58

Yellow:--- 18-----------9-----27

Green:----30----------18-----48

Total:----120-------- 116----236

Which of the following is the appropriate null hypothesis for addressing this question?

A. The distribution of color of first toy is the same for male and female toddlers.

B. Gender is dependent upon emotional association with the color of first toy.

C. Emotional associations with the color of first toy are independent of gender.

D. The number of observations in each cell is the same for each color.

E. 25% of all toddlers associate each color of their first toy.

A.

There are 2 populations and 1 variable. Therefore, this is a Chi-Square test for Homogeneity.

Null Hypothesis:

The distribution of color should be the same among each gender.