Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 456, if the null hypothesis is true: Expected Frequencies Over 65 years 45-65 years Chi-Square Distribution Degrees of Freedom = 4 л The chi-square statistic has been calculated for you: x² = 12.40. The distribution of the chi-square statistic has Use the following Distributions tool to find the critical value. Age Group 25-44 years 15-24 years 137.80 Because the chi-square statistic X² is 0 total US population. 1 2 63.52 .5000 With the level of significance a = 0.05, the critical value is 3 3.36 5000 4 Under 15 years 97.63 T 5 T 6 7 T 8 9 10 11 12 13 14 2² the critical value, you the null hypothesis. Therefore, you conclude that the proportions of left-handed people in the five age categories differ from the corresponding proportions for the degrees of freedom.

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Suppose you are reading a study conducted in the year 2000 about left-handed people in the United States. The authors report the following
frequency data on the age of the 456 lefties in their random sample:
Over 65 years
36
Over 65 years
12.43%
45-65 years
89
Observed Frequencies
Age Group
25-44 years
155
45-65 years
22.01%
You wonder if the age distribution of left-handed people matches the age distribution of the US population. You obtain the following data from the
2000 census:
15-24 years
68
Percent Distribution of the US Population by Age Group
Age Group
25-44 years
30.22%
Under 15 years
108
15-24 years Under 15 years
21.41%
13.93%
[Source: Hobbs F., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in the 20th century. US Census Bureau.]
You use a chi-square test for goodness of fit to see how well the sample of left-handed people fits the census data. What is the most appropriate
null hypothesis?
O The distribution of ages among left-handed people is equal across the five age categories.
O The distribution of ages among left-handed people is the same as that provided by the census data.
O The distribution of ages among left-handed people is different from that provided by the census data.
The distribution of ages among left-handed people is not equal across the five age categories.
Transcribed Image Text:Suppose you are reading a study conducted in the year 2000 about left-handed people in the United States. The authors report the following frequency data on the age of the 456 lefties in their random sample: Over 65 years 36 Over 65 years 12.43% 45-65 years 89 Observed Frequencies Age Group 25-44 years 155 45-65 years 22.01% You wonder if the age distribution of left-handed people matches the age distribution of the US population. You obtain the following data from the 2000 census: 15-24 years 68 Percent Distribution of the US Population by Age Group Age Group 25-44 years 30.22% Under 15 years 108 15-24 years Under 15 years 21.41% 13.93% [Source: Hobbs F., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in the 20th century. US Census Bureau.] You use a chi-square test for goodness of fit to see how well the sample of left-handed people fits the census data. What is the most appropriate null hypothesis? O The distribution of ages among left-handed people is equal across the five age categories. O The distribution of ages among left-handed people is the same as that provided by the census data. O The distribution of ages among left-handed people is different from that provided by the census data. The distribution of ages among left-handed people is not equal across the five age categories.
Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 456, if the null hypothesis
is true:
Expected Frequencies
Over 65 years 45-65 years
Chi-Square Distribution
Degrees of Freedom = 4
Age Group
25-44 years
The chi-square statistic has been calculated for you: x² = 12.40. The distribution of the chi-square statistic has
Use the following Distributions tool to find the critical value.
137.80
Because the chi-square statistic X² is
0
total US population.
15-24 years
1
2
63.52
.5000
With the level of significance a = 0.05, the critical value is
3
3.36
.5000
4
Under 15 years
97.63
5
6
7
8
9
10 11
12
13 14
X²
the critical value, you
the null hypothesis. Therefore, you
conclude that the proportions of left-handed people in the five age categories differ from the corresponding proportions for the
degrees of freedom.
Transcribed Image Text:Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 456, if the null hypothesis is true: Expected Frequencies Over 65 years 45-65 years Chi-Square Distribution Degrees of Freedom = 4 Age Group 25-44 years The chi-square statistic has been calculated for you: x² = 12.40. The distribution of the chi-square statistic has Use the following Distributions tool to find the critical value. 137.80 Because the chi-square statistic X² is 0 total US population. 15-24 years 1 2 63.52 .5000 With the level of significance a = 0.05, the critical value is 3 3.36 .5000 4 Under 15 years 97.63 5 6 7 8 9 10 11 12 13 14 X² the critical value, you the null hypothesis. Therefore, you conclude that the proportions of left-handed people in the five age categories differ from the corresponding proportions for the degrees of freedom.
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