Question

The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 96 Married, no children 29% 123 Single parent 9% 29 One person 25% 98 Other (e.g., roommates, siblings) 11% 65 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.) What are the degrees of freedom (c)Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

          The type of household for the U.S. population and for a random
sample of 411 households from a community in Montana are
shown below.
Type of Household
Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
96
Married, no children
29%
123
Single parent
9%
29
One person
25%
98
Other (e.g., roommates, siblings)
11%
65
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the Dove Creek
distribution.
(b) Find the value of the chi-square statistic for the
sample. (Round the expected frequencies to two decimal places.
Round the test statistic to three decimal places.)
What are the degrees of freedom
(c)Find or estimate the P-value of the sample test
statistic. (Round your answer to three decimal places.)

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Added by Josep M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Lucas Finney

05/01/2023

Step 1

First, we need to find the expected number of households in the community for each type of household based on the U.S. population percentages. Expected Number of Households in the Community: - Married with children: 0.26 * 411 = 106.86 - Married, no children: Show more…

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The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 96 Married, no children 29% 123 Single parent 9% 29 One person 25% 98 Other (e.g., roommates, siblings) 11% 65 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.) What are the degrees of freedom (c)Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

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00:01 For this problem to begin, i'll note that we find our chi -squared statistic by taking the sum over all of the categories, so sum from i equals 1 to k, where we have k different categories, of the observed frequency minus the expected frequency, squared, divided by the expected frequency, where we'll find our expected frequencies by taking the total sample size, n, times the expected proportion, where we find our expected proportions from the household percent, or from the percent of u .s.

00:35 Households column.

00:37 So for actually calculating this out, i'll jump over into excel.

00:41 So setting everything up here, we have the percent, then i'll have the expected, the observed, then o minus e squared over e.

00:56 So the percentages are, let's see here, 0 .26, 0 .29, 0 .09, 0 .25, 0 .11.

01:06 We find the expected frequencies by taking the percentages and multiplying them by, well, we're told that we have 411 households in the sample, so we multiply each by 411.

01:18 So we have our expected frequencies, shown here, then the observed frequencies are the frequencies from the community in montana.

01:28 So we have, let's see here, 96, 123, 29, did i miss one? 29, 98, 65.

01:41 No, it does not look like i missed one, but i'm just going to double check.

01:44 So we have married with children, married, no children, single parent, one person, and other.

01:48 Okay, yeah, there we go.

01:50 Then, we calculate out the standardized residuals for each...

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