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Chi-Squared Quiz IB MAI SL

Total questions: 25

Worksheet time: 32mins

Name
Class
Date
1.

How many degrees of freedom will be present?

a)

4

b)

5

c)

6

d)

7

2.
The bigger the chi square statistic, the ________ the p value.
a)
bigger
b)
smaller
3.
A chi-square test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely).  The spinner is spun 100 times, and the results are recorded.  The degrees of freedom for the test will be
a)
8
b)
9
c)
10
d)
99
4.

Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch. The one-way table below displays the sample data. What is the appropriate null hypothesis

a)

U1-U2=U3=U4

b)

Mixed nut proportions are proportioned the same as they claim

c)

At least one of the four types in the population is different than expect

d)

the observed counts are equally distributed

5.

Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs that hatched and didn’t hatch.

If the p-value is .08 and you use .05 as your alpha, what is your conclusion

a)

Fail to reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options

b)

Reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options

c)

Fail to reject: We do have sufficient evidence that distribution of hatched is different for water temperature options

6.

For this Chi-Square Goodness of Fit Test, how many degrees of freedom are there?

a)

1

b)

2

c)

3

d)

More information is needed to determine.

7.

Which of the following makes for a reasonable null hypothesis for a Chi-Square Goodness of Fit Test?

a)

The distribution of political views this year is 0.24 liberal, 0.38 moderate, 0.38 conservative.

b)

The distribution of political views this year differs from a distribution of 0.24 liberal, 0.38 moderate, 0.38 conservative.

c)

The distribution of political views this year is independent of gender.

d)

This is not a situation where using a Chi-Square Goodness of Fit Test is appropriate.

8.

Given a significance level of 5%, should we accept or reject the null hypothesis.

a)

Since the p-value of 0.231 is greater than the significance level of 0.05, we should accept the null hypothesis.

b)

Since the p-value of 0.447 is greater than the significance level of 0.05, we should accept the null hypothesis.

c)

Since the p-value of 0.231 is less than the significance level of 5%, we should accept the null hypothesis.

d)

Since the p-value of 0.447 is greater than the significance level of 0.05, we should reject the null hypothesis.

9.
What are the expected counts of a female who likes Pepsi?
a)
10.5
b)
11
c)
14.5
d)
6.3
10.

What is the null hypothesis?

a)

Injury type is independent of position played

b)

Injury type is dependent on the position played independent

c)

Injury type is correlated to position played.

d)

There is no difference between categories

11.

Find the chi-squared calculated value for the table.

a)

0.486170447

b)

1.442392006

c)

1.45

d)

2

12.

For a p-value from the calculator of 1.32355E-3 what would the conclusion be if testing at 10% significance level?

a)

Accept Ho

b)

Reject H1

c)

Reject Ho

d)

Need to know the chi-squared number

13.

If the χ2 critical value = 5.99 and the

χ2 calculated value = 7.35, what is the conclusion

a)

Reject Ho, accept H1

b)

Accept Ho, reject H1

c)

there is not enough info to decide

d)

The conclusion can only be made if we also know the p-value

14.

Which test would you use to see if age is a factor choosing a person’s favorite fruit? 900 college students were surveyed and their favorite fruit recorded.

a)

Chi-square Goodness of Fit Test

b)

Correlation coefficient

c)

Chi-Square Test for Independence

d)

Chi-square test for correlation

15.

Which test would you use to see whether the fans that buy tickets are demographically the same as the general population of the city. Currently 42% are Caucasian, 35% are Latinx, 12% are African American, 8% are Asian, and the rest are defined as other.

a)

Chi-square Goodness of Fit Test

b)

Chi-Square Test for Independence/Association

c)

Not a Chi-square test

16.

A chi-square test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

a)

8

b)

9

c)

10

d)

99

17.

In 1974, each acre of the Tahoe basin was assessed to see what condition the soil was in. 23% of acres were of type I, 32% were of type II, 41% were of type III, and 16% were of type IV. This year the region was assessed again and the number of each type were again determined.

a)

Chi-square Goodness of Fit Test

b)

Chi-Square Test for Homogeneity

c)

Chi-Square Test for Independence

d)

Not a Chi-square test

18.

Is the type of music that people listen to related to the state that they were born in? 10,000 Americans were asked what type of music they listened to and where they were born.

a)

Chi-square Goodness of Fit Test

b)

Chi-Square Test for Homogeneity

c)

Chi-Square Test for Independence

d)

Not a Chi-square test

19.
The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year.  She wants to know if each type of food will be equally popular so she can start ordering supplies making other plans.  To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?"  Here are the data in the table provided.  The P-value for a chi-square test for goodness of fit is 0.0129.  Which is the following is the most appropriate conclusion?
a)
Because 0.0129 is less than α = 0.05, reject H0.  There is convincing evidence that the food choices are equally popular.
b)
Because 0.0129 is less than α = 0.05, reject H0.  There is not convincing evidence that the food choices are equally popular.
c)
Because 0.0129 is less than α = 0.05, reject H0.  There is convincing evidence that the food choices are not equally popular.
d)
Because 0.0129 is less than α = 0.05, fail to reject H0.  There is convincing evidence that the food choices are equally popular.
20.

The table shows the number or babies born on each day of the week. Is there evidence that births are more likely on specific days of the week?

a)

yes, the p value is greater than .05

b)

no evidence, the p value is less than .05

c)

yes, the p value is less than .05

d)

no evidence, the p value is greater than .05

21.

In both chi square tests, observed frequencies and expected frequencies are used to calculate the p-value

a)

True

b)

False

22.

Mr. V asks his class what their favorite ice cream flavor is. He wonders if the flavors are equally represented. The table shows the observed values. What should be the expected counts of each flavor if they are equally represented?

a)

40

b)

20

c)

4

d)

3

23.

Mr. V asks his class what their favorite ice cream flavor is. He wonders if the flavors are equally represented. The table shows the observed values. What should be the H0 and the HA?

a)

H0: The distribution of flavors is approximately normal.

HA: The distribution of flavors is not approximately normal.

b)

H0: The distribution of flavors is equal.

HA: The distribution of flavors is not equal.

c)

H0: The distribution of flavors is homogenous.

HA: The distribution of flavors is not homogenous.

d)

H0: The distribution of flavors is independent.

HA: The distribution of flavors is not independent.

24.

Mr. V asks his class what their favorite ice cream flavor is. He wonders if the flavors are equally represented. The table shows the observed values. How many degrees of freedom are there?

a)

4

b)

3

c)

2

d)

1

25.

Mr. V asks his class what their favorite ice cream flavor is. He wonders if the flavors are equally represented. The table shows the observed values. What is the Chi Square statistic?

a)

4.4

b)

0.221

c)

3

d)

3.2