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
Question
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
Solution
This question is asking for a statistical analysis of the data provided.
Part 1:
The expected frequency (fE) for each category is calculated based on the popular conception at the magazine. So, for weddings in a church, it's 50% of 280, which is 140. For weddings indoors but not in a church, it's 30% of 280, which is 84. For outdoor weddings, it's 20% of 280, which is 56.
The observed frequency (fO) is given in the question.
The value of -fO/fE^2 is calculated by subtracting the observed frequency from the expected frequency, squaring the result, and then dividing by the expected frequency.
So, for weddings in a church, it's (140-146)^2 / 140 = 0.257. For weddings indoors but not in a church, it's (84-72)^2 / 84 = 1.714. For outdoor weddings, it's (56-62)^2 / 56 = 0.643.
Part 2:
(a) The type of test statistic to use is Chi-square. The degrees of freedom is the number of categories minus 1, so in this case it's 3-1 = 2.
(b) The value of the test statistic is the sum of the -fO/fE^2 values, so it's 0.257 + 1.714 + 0.643 = 2.614.
(c) The critical value for a Chi-square test with 2 degrees of freedom at the 0.05 level of significance is 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 that the actual distribution of first wedding locations matches the distribution in the magazine's popular conception. So, the answer is No, we cannot conclude that the actual distribution of location of first weddings is different from the distribution in the magazine's popular conception.
Similar Questions
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
A psychology researcher was conducting a study about newlywed heterosexual couples during the first two years of their marriage. 513 newlywed couples were randomly chosen for the study. One of the questions that the researcher was interested in was "During a typical week, how many times do you have sex?" The 513 responses had an average of 2.35 and standard deviation of 1.2. Another question that was asked is "During a typical week, how many evenings do you go out?" 171 of the couples answered that they go out more than twice a week.What is the point estimate for the proportion of all newlyweds who go out more than twice during a typical week?
Jonide comes across a newspaper article with the headline, “Bigger Weddings Lead to Happier Marriages.” She reads that researchers recruited 418 married couples from a local shopping center and collected their responses to a variety of survey questions, including some asking about the number of guests at their wedding and their relationship happiness (measured with questions about spousal satisfaction). This table presents the results of the study.CRITERION(DEPENDENT)VARIABLE:RELATIONSHIP HAPPINESS BETA 95% CIFOR BETAPredictor(independent)variables:Number of guests at wedding 0.32 [.12, .52]Number of partners before marriage 0.42 [.22, .62]Years of education 0.13 [.01, .25]Personal income –0.21 [–.37, –.07]Religiosity 0.06 [–.15, .27]Identify the validities that are reasonably established in this study.
Compared to couples who meet in other, conventional ways, couples who meet online __________.A.typically marry after a longer period of timeB.are less likely to marryC.are almost all over the age of sixty-fiveD.are less likely to already have friends in common
A large university took a random sample of the students and found that 35% were married. The researcher wondered if that proportion was the same for the entire student population. When the marriage records of all students were checked, the researcher found out that 31% of the students were married. Which of the following is the correct statement?Group of answer choicesBoth 35% and 31% are statisticsThe 35% is a statistic and 31% is the parameterBoth 35% and 31% are parametersThe 31% is a statistic and the 35% is the parameter
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.