The Chi-Square Test for Goodness of Fit

The chi-square test for goodness of fit

Video Player is loading.

Current Time 0:00

Duration 0:00

Loaded: 0%

Stream Type LIVE

Remaining Time 0:00

Question 1

146

Question 1.

True or false: A chi-square goodness of fit test is only performed on one-sample categorical data with three or more categories.

False

True

Incorrect. This is the basic application of a chi-square goodness of fit test.

Correct. This is the basic application of a chi-square goodness of fit test.

Incorrect. Try again.

Question 2

271

Question 2.

Why should we use a chi-square goodness of fit test to answer the question given in Example 5?

Example 5: “Do the colors of M & M’s in a 16 ounce bag follow the proportions for colors published on the M & M website?”

There are two types of M & M's with three or more colors.

It is one sample of M & M's with more than two colors.

It is two samples of M & M's with three or more colors.

Incorrect. A chi-square goodness of fit test is performed on data from one sample that can be categorized into three or more categories. One 16 ounce bag gives one sample with three or more colors so the counts of M & M's in the color categories should be compared with a chi-square goodness of fit test.

Correct. A chi-square goodness of fit test is performed on data from one sample that can be categorized into three or more categories. One 16 ounce bag gives one sample with three or more colors so the counts of M & M's in the color categories should be compared with a chi-square goodness of fit test.

Incorrect. Try again.

Question 3

427

Question 3.

Fill in the blank: The data for a one sample z test for proportion has ___________ categories whereas the data for a chi-square goodness of fit test has _______________ categories.

more than two, two

two, more than two

Incorrect. The data for a one-sample t test for proportion has only two categories whereas the data for a chi-square goodness of fit test has three or more categories.

Correct. The data for a one-sample t test for proportion has only two categories whereas the data for a chi-square goodness of fit test has three or more categories.

Incorrect. Try again.

Question 4

507

Question 4.

How should data be collected for a chi-square goodness of fit test?

Randomized order of applying two treatments to each individual in a matched pairs design

Random allocation of individuals to two or more treatments

One simple random sample

Separate simple random samples—one from each population

Incorrect. Data for a chi-square goodness of fit test should be collected with a simple random sample and the response variable must be categorical with three or more categories.

Correct. Data for a chi-square goodness of fit test should be collected with a simple random sample and the response variable must be categorical with three or more categories.

Incorrect. Try again.

Question 5

565

Question 5.

According to this outline, what are the degrees of freedom for a chi-square goodness of fit test statistic?

n₁ + n₂ - 2

(r - 1)(c - 1)

n - 1

k - 1

Incorrect. The degrees of freedom for the chi-square goodness of fit test statistic are k - 1, where k = number of categories.

Correct. The degrees of freedom for the chi-square goodness of fit test statistic are k - 1, where k = number of categories.

Incorrect. Try again.

Question 6

610

Question 6.

If students choose numbers between one and seven randomly, what is the probability that a randomly selected student picks a three?

One out of seven or

$\frac{1}{7}$ .

One out of three or

$\frac{1}{3}$ .

One out of ten or

$\frac{1}{10}$ .

Incorrect. Since there are seven numbers and they are to be picked randomly, the probability of a randomly selected student picking a three is

$\frac{1}{7}$ or 0.143.

Correct. Since there are seven numbers and they are to be picked randomly, the probability of a randomly selected student picking a three is

$\frac{1}{7}$ or 0.143.

Incorrect. Try again.

Question 7

666

Question 7.

If students do indeed pick numbers between one and seven randomly (H₀: p_i = $\frac{1}{7}$ ), how many students do we expect to pick a "three?"

$\frac{1}{10}$ (101)

$\frac{1}{3}$ (101)

$\frac{1}{7}$ (101)

Incorrect. If students pick numbers randomly, then each number has probability

$\frac{1}{7}$ of being selected. So, we expect

$\frac{1}{7}$ (101) = 14.43 out of 101 to pick the number "three."

Correct. If students pick numbers randomly, then each number has probability

$\frac{1}{7}$ of being selected. So, we expect

$\frac{1}{7}$ (101) = 14.43 out of 101 to pick the number "three."

Incorrect. Try again.

Question 8

709

Question 8.

On the basis of this graphic, which number is chosen more often than expected?

One

Three

Seven

Incorrect. The number three is selected 27 times and only expected to be selected 14.43 times.

Correct. The number three is selected 27 times and only expected to be selected 14.43 times.

Incorrect. Try again.

Question 9

737

Question 9.

Are the expected counts big enough so that the chi-square distribution is a good approximation for the chi-square test statistic?

Yes

Incorrect. Since the expected counts are 14.43, they are all bigger than five and the approximation will be good.

Correct. Since the expected counts are 14.43, they are all bigger than five and the approximation will be good.

Incorrect. Try again.

Question 10

832

Question 10.

If 0.0025 < P-value < 0.005 and α = 0.05, should we reject H₀?

Yes

Incorrect. Since 0.0025 < P-value < 0.005 is less than α = 0.05, we reject H₀.

Correct. Since 0.0025 < P-value < 0.005 is less than α = 0.05, we reject H₀.

Incorrect. Try again.

Question 11

888

Question 11.

True or false: Students are more likely to pick the numbers one or seven than the numbers in between.

False

True

Incorrect. Actually, students are less likely to pick the numbers one or seven and more likely to pick numbers in the middle.

Correct. Actually, students are less likely to pick the numbers one or seven and more likely to pick numbers in the middle.

Incorrect. Try again.

StatTutor Lesson - The Chi-Square Test for Goodness of Fit

Question 1

Question 1.

Question 2

Question 2.

Question 3

Question 3.

Question 4

Question 4.

Question 5

Question 5.

Question 6

Question 6.

Question 7

Question 7.

Question 8

Question 8.

Question 9

Question 9.

Question 10

Question 10.

Question 11

Question 11.