# Chapter 1. The Chi-Square Test for Goodness of Fit

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Stat Tutor
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2:26

### Question 1.1

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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.
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4:31

### Question 1.2

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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.
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7:07

### Question 1.3

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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.
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8:27

### Question 1.4

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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.
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9:25

### Question 1.5

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.
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10:10

### Question 1.6

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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.
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11:06

### Question 1.7

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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.

11:49

### Question 1.8

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.
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12:17

### Question 1.9

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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.
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13:52

### Question 1.10

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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.
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14:48