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Matrimony Monthly is a magazine that provides information for couples thinking about marriage. Over the years, writers for the magazine have researched just about everything there is to research about weddings. The popular conception at the magazine has been that roughly 50% of first weddings take place indoors in a church, 30% take place indoors in a building other than a church, and 20% take place outdoors. This past week, the magazine examined a random sample of 280 first weddings and found the distribution given by the first row of numbers in the table below. (This row contains the frequencies observed in their sample of 280.) The second row of numbers gives the frequencies expected under the hypothesis that the popular conception at the magazine is correct. The bottom row of numbers contains the following value for each of the wedding location categories.−fOfE2fE= −Observed frequencyExpected frequency2Expected frequencyPart 1Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your −fOfE2fE responses to three or more decimal places.Send data to ExcelIn a church Indoors but not in a church Outdoors TotalObserved frequencyfO fO146 fO72 fO62 280Expected frequencyfE fE fE84.00 fE −fOfE2fE −fOfE2fE −fOfE2fE1.714 −fOfE2fE Part 2Answer the following to summarize the test of the hypothesis that the actual distribution of first wedding locations matches the distribution in the magazine's popular conception. Use the 0.05 level of significance for the test.(a)  Determine the type of test statistic to use.Type of test statistic: ▼(Choose one)(b)  Find the value of the test statistic. (Round your answer to two or more decimal places.)(c)  Find the critical value. (Round your answer to two or more decimal places.)(d)Can we conclude that the actual distribution of location of first weddings is different from the distribution in the magazine's popular conception?Yes No

Question

Matrimony Monthly is a magazine that provides information for couples thinking about marriage. Over the years, writers for the magazine have researched just about everything there is to research about weddings. The popular conception at the magazine has been that roughly 50% of first weddings take place indoors in a church, 30% take place indoors in a building other than a church, and 20% take place outdoors. This past week, the magazine examined a random sample of 280 first weddings and found the distribution given by the first row of numbers in the table below. (This row contains the frequencies observed in their sample of 280.) The second row of numbers gives the frequencies expected under the hypothesis that the popular conception at the magazine is correct. The bottom row of numbers contains the following value for each of the wedding location categories.−fOfE2fE= −Observed frequencyExpected frequency2Expected frequencyPart 1Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your −fOfE2fE responses to three or more decimal places.Send data to ExcelIn a church Indoors but not in a church Outdoors TotalObserved frequencyfO fO146 fO72 fO62 280Expected frequencyfE fE fE84.00 fE −fOfE2fE −fOfE2fE −fOfE2fE1.714 −fOfE2fE Part 2Answer the following to summarize the test of the hypothesis that the actual distribution of first wedding locations matches the distribution in the magazine's popular conception. Use the 0.05 level of significance for the test.(a)  Determine the type of test statistic to use.Type of test statistic: ▼(Choose one)(b)  Find the value of the test statistic. (Round your answer to two or more decimal places.)(c)  Find the critical value. (Round your answer to two or more decimal places.)(d)Can we conclude that the actual distribution of location of first weddings is different from the distribution in the magazine's popular conception?Yes No

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Solution

This question is asking for a Chi-Square Goodness of Fit test.

Part 1:

The expected frequencies (fE) are calculated based on the popular conception at the magazine.

For "In a church", it's 50% of 280, which is 140. For "Indoors but not in a church", it's 30% of 280, which is 84. For "Outdoors", it's 20% of 280, which is 56.

The formula for the last row is (Observed frequency - Expected frequency)^2 / Expected frequency.

For "In a church", it's (146-140)^2 / 140 = 0.257. For "Indoors but not in a church", it's (72-84)^2 / 84 = 1.714. For "Outdoors", it's (62-56)^2 / 56 = 0.643.

Part 2:

(a) The type of test statistic to use is Chi-Square.

(b) The value of the test statistic is the sum of the last row, which is 0.257 + 1.714 + 0.643 = 2.614.

(c) The critical value for a Chi-Square distribution with 2 degrees of freedom (3 categories - 1) at the 0.05 level of significance is approximately 5.991.

(d) Since the value of the test statistic (2.614) is less than the critical value (5.991), we cannot reject the null hypothesis. Therefore, we cannot conclude that the actual distribution of location of first weddings is different from the distribution in the magazine's popular conception.

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Question 1Matrimony Monthly is a magazine that provides information for couples thinking about marriage. Over the years, writers for the magazine have researched just about everything there is to research about weddings. The popular conception at the magazine has been that roughly 50% of first weddings take place indoors in a church, 30% take place indoors in a building other than a church, and 20% take place outdoors. This past week, the magazine examined a random sample of 280 first weddings and found the distribution given by the first row of numbers in the table below. (This row contains the frequencies observed in their sample of 280.) The second row of numbers gives the frequencies expected under the hypothesis that the popular conception at the magazine is correct. The bottom row of numbers contains the following value for each of the wedding location categories.−fOfE2fE= −Observed frequencyExpected frequency2Expected frequencyPart 1Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your −fOfE2fE responses to three or more decimal places.Send data to ExcelIn a church Indoors but not in a church Outdoors TotalObserved frequencyfO fO146 fO72 fO62 280Expected frequencyfE fE84 fE84.00 fE84 −fOfE2fE −fOfE2fE56 −fOfE2fE1.714 −fOfE2fE56 Part 2Answer the following to summarize the test of the hypothesis that the actual distribution of first wedding locations matches the distribution in the magazine's popular conception. Use the 0.05 level of significance for the test.(a)  Determine the type of test statistic to use.Type of test statistic: ▼Chi-squareDegrees of freedom: (b)  Find the value of the test statistic. (Round your answer to two or more decimal places.)2.614(c)  Find the critical value. (Round your answer to two or more decimal places.)5.991(d)Can we conclude that the actual distribution of location of first weddings is different from the distribution in the magazine's popular conception?Yes No

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