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Elementary Statistics: Picturing the World

Ron Larson, Betsy Farber

Chapter 10

Chi-Square Tests and the F-Distribution - all with Video Answers

Educators

Section 1

Goodness-of-Fit Test

01:31

Problem 1

What is a multinomial experiment?

Harsh Gadhiya
Harsh Gadhiya
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01:10

Problem 2

What conditions are necessary to use the chi-square goodness-of-fit test?

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Harsh Gadhiya
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00:45

Problem 3

Find the expected frequency for the values of $n$ and $p_{i}$
$$n=150, p_{i}=0.3$$

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Harsh Gadhiya
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01:06

Problem 4

Find the expected frequency for the values of $n$ and $p_{i}$
$$n=500, p_{i}=0.9$$

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Harsh Gadhiya
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01:48

Problem 5

Find the expected frequency for the values of $n$ and $p_{i}$
$$n=230, p_{i}=0.25$$

Harsh Gadhiya
Harsh Gadhiya
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01:48

Problem 6

Find the expected frequency for the values of $n$ and $p_{i}$
$$n=415, p_{i}=0.08$$

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Harsh Gadhiya
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12:49

Problem 7

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A researcher claims that the ages of people who go to movies at least once a month are distributed as shown in the figure. You randomly select 1000 people who go to movies at least once a month and record the age of each. The table shows the results. At $\alpha=0.10,$ test the researcher's claim.
(IMAGE CAN'T COPY)
(TABLE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
12:56

Problem 8

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A researcher claims that the numbers of cups of coffee U.S. adults drink per day are distributed as shown in the figure. You randomly select 1600 U.S. adults and ask them how many cups of coffee they drink per day. The table shows the results. At $\alpha=0.05,$ test the researcher's claim.
(FIGURE CAN'T COPY)

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Harsh Gadhiya
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14:34

Problem 9

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A research firm claims that the distribution of the days of the week that people are most likely to order food for delivery is different from the distribution shown in the figure. You randomly select
500 people and record which day of the week each is most likely to order food for delivery. The table shows the results. At $\alpha=0.01,$ test the research firm's claim.
(FIGURE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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13:53

Problem 10

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A personnel director claims that the distribution of the reasons workers leave their jobs is different from the distribution shown in the figure. You randomly select 200 workers who recently left their jobs and record each worker's reason for doing so. The table shows the results. At $\alpha=0.01,$ test the personnel director's claim.
(FIGURE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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13:11

Problem 11

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A researcher claims that the number of homicide crimes in California by season is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the season when each happened. The table shows the results. At $\alpha=0.05,$ test the researcher's claim.
(FIGURE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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17:41

Problem 12

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A researcher claims that the number of homicide crimes in California by month is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the month when each happened. The table shows the results. At $\alpha=0.10,$ test the researcher's claim.
(TABLE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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18:27

Problem 13

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
The pie chart shows the distribution of the opinions of U.S. parents on whether a college education is worth the expense. An economist claims that the distribution of the opinions of U.S. teenagers is different from the distribution for U.S. parents. To test this claim, you randomly select 200 U.S. teenagers and ask each whether a college education is worth the expense. The table shows the results. At $\alpha=0.05,$ test the economist's claim.
(FIGURE CAN'T COPY)
(TABLE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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18:43

Problem 14

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
The pie chart shows the distribution of how much married U.S. male adults trust their spouses to manage their finances. A financial services company claims that the distribution of how much married
U.S. female adults trust their spouses to manage their finances is the same as the distribution for married U.S. male adults. To test this claim, you randomly select 400 married U.S. female adults and ask each how much she trusts her spouse to manage their finances. The table shows the results. At $\alpha=0.10,$ test the company's claim.
(FIGURE CAN'T COPY)
(TABLE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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15:17

Problem 15

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
An organization claims that the number of prospective home buyers who want their next house to be larger, smaller, or the same size as their current house is not uniformly distributed. To test this claim, you randomly select 800 prospective home buyers and ask them what size they want their next house to be. The table at the left shows the results. At $\alpha=0.05,$ test the organization's claim.

Harsh Gadhiya
Harsh Gadhiya
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15:04

Problem 16

(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A doctor claims that the number of births by day of the week is uniformly distributed. To test this claim, you randomly select 700 births from a recent year and record the day of the week on which each takes place. The table shows the results. At $\alpha=0.10,$ test the doctor's claim.
(TABLE CAN'T COPY)

Harsh Gadhiya
Harsh Gadhiya
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02:06

Problem 17

In Exercises 17 and $18,(a)$ find the expected frequencies, $(b)$ find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
At $\alpha=0.01,$ test the claim that the 200 test scores shown in the frequency distribution are normally distributed.
(TABLE CAN'T COPY)

Qudsiya Anis
Qudsiya Anis
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01:58

Problem 18

Find the expected frequencies, $(b)$ find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
At $\alpha=0.05,$ test the claim that the 400 test scores shown in the frequency distribution are normally distributed.
(TABLE CAN'T COPY)

Qudsiya Anis
Qudsiya Anis
Numerade Educator