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Exam 12: Chi-Square Tests

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Question 31

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MARS claims that Skittles candies should be comprised of 30% purple, 10% orange, and 20% should be red, yellow, and green. Business students count a large bag of Skittles and find 265 red, 279 purple, 303 yellow, 271 green, and 212 orange candies. A) Set up the competing hypotheses to test if at least one proportion is different than the value claimed by MARS. B) Calculate the value of the test statistic and determine the degrees of freedom. C) Compute the p-value. Does the evidence suggest that at least one proportion is different from the claimed value at the 5% significance level?

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a. H₀: p_p = 0.30, p_o = 0.10, p_r = 0.20, p_y = ...

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Question 32

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In the following table, individuals are cross-classified by their age group and income level. Assuming age group and income are independent, the expected "low income and 21-35 age group" cell frequency is ________.

A) 105.27
B) 107.72
C) 146.31
D) 178.42

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Question 33

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The heights (in cm) for a random sample of 60 male employees of S&M Construction Company were measured. The sample mean is 166.5, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. Suppose the null hypothesis of normality is rejected. Which of the following is a valid conclusion?

A researcher wants to determine if the distribution of races hired at government agencies is reflective of the overall U.S. population demographics. The researcher uses census data on demographics to obtain proportions for different races. The following table shows these proportions and the number of each race hired for a particular government agency. a. Set up the competing hypotheses to test if at least one proportion is different from the population demographics. B) Calculate the value of the test statistic and determine the degrees of freedom. C) Compute the p-value. Does the evidence suggest at least one proportion is different from the population demographics at the 1% significance level?

The airline industry defines "no-shows" as passengers who have purchased a ticket but fail to arrive at the gate on time for departure. United Airlines operates many flights from Philadelphia to Dallas. The table below represents the observed number of no-shows that occurred on a random sample of 120 flights between Philadelphia and Dallas this year, and experienced the no-show proportions last year. United Airlines would like to know if the proportions of no-shows has changed between last year and this year on flights between these two cities using α = 0.05. The test statistic for this sample is ________.

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. The p-value is ________.

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Using the critical value approach, the decision and conclusion are ________.

For the goodness-of-fit test for normality, the null and alternative hypotheses are ________.

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. The expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is ________.

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Using the p-value approach and α = 0.05, the decision and conclusion are ________.

For the chi-square test for normality, the expected frequencies for each interval must be ________.

The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals. Using the p-value approach and α = 0.05, the decision and conclusion are ________.

Which of the following null hypotheses is used to test if five population proportions are the same?

For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom.

A travel agent wants to determine if clients have a preference of four different airlines. For a sample of 200 flight reservations, there were 70, 45, 48, and 37 reservations for the four different airlines. A) Set up the competing hypotheses to test if the population proportions are not equal to each other. B) Calculate the value of the test statistic. C) Specify the critical value at the 5% significance level. D) What is the conclusion of the hypothesis test?

The airline industry defines "no-shows" as passengers who have purchased a ticket but fail to arrive at the gate on time for departure. United Airlines operates many flights from Philadelphia to Dallas. The table below represents the observed number of no-shows that occurred on a random sample of 120 flights between Philadelphia and Dallas this year, and experienced the no-show proportions last year. United Airlines would like to know if the proportions of no-shows has changed between last year and this year on flights between these two cities using α = 0.05. The expected frequency of five no-shows for this sample is ________.

In the following table, likely voters' preferences of two candidates are cross-classified by gender. For the chi-square test of independence, the value of the test statistic is ________.

The heights (in cm) for a random sample of 60 males were measured. The sample mean is 166.55, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The following table shows the heights subdivided into non-overlapping intervals. Suppose the value of the test statistic is 7.71. Using the critical value approach, decision and conclusion are ________.

The airline industry defines "no-shows" as passengers who have purchased a ticket but fail to arrive at the gate on time for departure. United Airlines operates many flights from Philadelphia to Dallas. The table below represents the observed number of no-shows that occurred on a random sample of 120 flights between Philadelphia and Dallas this year, and experienced the no-show proportions last year. United Airlines would like to know if the proportion of no-shows has changed between last year and this year on flights between these two cities using α = 0.05. The conclusion for this hypothesis would be that because the test statistic is ________.

A fund manager wants to know if it is equally likely that the Dow Jones Industrial Average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Dow Jones Industrial Average goes up. For the goodness-of-fit test, what are the degrees of freedom for the chi-squared test statistic?