Exam 15: Chi-Squared Tests Optional

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Consumer panel preferences for three proposed Cafes are as follows: Cafe A Cafe B Cafe C 48 62 40 Use 0.05 level of significance and test to see if there is a preference among the three Cafes, according to the data.

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NARRBEGIN: Students Absenteeism Student Absenteeism Consider a multinomial experiment involving n = 200 students of a large high school. The attendance department recorded the number of students who were absent during the weekdays. The null hypothesis to be tested is: H0: p1 = 0.10, p2 = 0.25, p3 = 0.30, p4 = 0.20, p5 = 0.15.NARREND -{Student Absenteeism Narrative} Test the hypothesis at the 5% level of significance with the following frequencies: Day of the Week Mon. Tues. Wed. Thurs. Fri Number Absent 22 28 24 18

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What statistic do we get when we square the value of z?

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The number of degrees of freedom in testing for normality is the:

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The number of ATVs sold by three salespersons over a 3-month period is shown below: Brand of ATV Falesparson Brand Brand Brand Juan 7 2 6 pedro 11 4 Fernando 5 3 Use the 5% level of significance and test for the independence of salesperson and type of product sold.

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In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 500 observations. In addition, the researcher used 6 standardized intervals to test for normality. Using a 5% level of significance, the critical value for this test is:

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Which of the following statements regarding the chi-squared distribution is true?

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The Chairman of a committee has recently circulated pamphlets among the members, attempting to convince them that pension benefits should be the primary issue. A subsequent survey revealed the following breakdown of the members according to the plant at which they worked and the issue that they felt should be supported as the primary one. Issues Plant Location Very Interesting Fairly Interesting Not Interesting New Mexico 60 62 78 Utah 70 56 74 Do the data indicate at the 5% significant level that there are differences between the two plants regarding which issue should be the primary one?

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In 2011, computers of Brand A controlled 25% of the market, Brand B 20%, Brand C 10%, and brand D 45%. In 2015, sample data was collected from many randomly selected stores throughout the country. Of the 1,200 computers sold, 280 were Brand A, 270 were Brand B, 90 were Brand C, and 560 were Brand D. Has the market changed since 2011? Test at the 1% significance level.

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If you want to compare two populations that each have two categories, which test(s) can you use?

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A test for the differences between two proportions can be performed using the chi-squared distribution.

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How do you find the probabilities needed to obtain expected frequencies for a test of a contingency table?

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To describe a population with more than two categories you can only use a chi-squared goodness-of-fit test.

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The chi-squared test of a contingency table is based upon:

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In a test of a contingency table, rejecting the null hypothesis concludes the variables are not independent.

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In a chi-squared test of a contingency table, the value of the test statistic was χ\chi 2 = 15.652, and the critical value at α\alpha = 0.025 was 11.1433. Thus, we must reject the null hypothesis at α\alpha = 0.025.

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A chi-squared test of a contingency table can be used to infer that differences exist between ____________________ populations of nominal variables.

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The number of degrees of freedom for a contingency table with 4 rows and 8 columns is

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To determine the critical values in the chi-squared distribution table, you need to know the:

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For comparing two or more populations each having two or more categories, use a(n) ____________________ test of a(n) ____________________.

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