Exam 11: Other Chi-Square Tests

Chicken, hot dogs, and hamburgers were served during a recent barbecue. The host assur there would be no difference between what the women chose to eat and what the men cho eat. Compute the test value for the following data. Chicken Hot Dogs Hamburgers Women 7 3 4 Men 4 5 6

The following table presents the numbers of cucumber seeds, by brand, that germinated o to germinate 14 days after planting. Brand A Brand B Brand C Brand D Germinated 35 36 45 30 Failed to Germinate 13 11 10 7 Can you conclude that the the germination rate is related to the brand of seed? Use the $\alpha = 0.05$ level of significance.

Before computing the test value, one should state the hypothesis.

Frequencies obtained by calculation are called expected frequencies.

The following table presents the numbers of customers who - after 2 weeks of use - were or dissatisfied with their newly-purchased computers. Brand A Brand B Brand C Brand D Satisfied 38 26 21 44 Dissatisfied 3 9 13 9 Can you conclude that the the satisfaction rate is related to the brand of computer? Use thi $\alpha = 0.05$ level of significance.

A random group of students was asked to name their favorite type of music. The campus radio station believes that $16 \%$ of the students prefer rap, $26 \%$ prefer rock, $15 \%$ country, $11 \%$ prefer new age, and $32 \%$ prefer oldies. Is there evidence to reject this hypothesis at $\alpha = 0.05$ ? Type of music Rap Rock Country New Age Oldies Number of Students 24 29 18 20 18

The number of visits to a certain web site were counted each day of a particular w The results are given in the following table. Day Number of Visits Sunday 140 Monday 121 Tuesday 113 Wednesday 110 Thursday 130 Friday 134 Saturday 140 Test the hypothesis that the web site visits are equally likely to occur on any day o week. Use the $\alpha = 0.01$ level of significance.

The critical chi-square value for 15 degrees of freedom when $\alpha = 0.05$ and the test is right-tailed is $19.675$ .

For the given table of observed frequencies: 1 2 3 A 60 61 53 B 87 90 81 C 41 94 82 i). Compute the row totals, the column totals, and the grand total. ii). Construct the corresponding table of expected values. iii). Compute the value of the chi-square test statistic. iv). Perform a test for independence, using the $\alpha = 0.05$ level of significance.

A biology professor claims that, on the average, $15 \%$ of her students get a grade of $\mathrm { A }$ , $30 \%$ get a $\mathrm { B } , 30 \%$ get a $\mathrm { C } , 10 \%$ get a D, and $15 \%$ get an $\mathrm { F }$ . The grades of a random sample of 105 students were recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 17 39 26 5 18 Test the hypothesis that the grades follow the distribution claimed by the professor. Use tl $\alpha = 0.01$ level of significance.

A random group of oranges were selected from an orchard to analyze their ripeness. Based on the time of year, the orchard owner believes that $35 \%$ of the oranges are ready for picking now, $30 \%$ will be ready in three days, $20 \%$ will be ready in one week, and $15 \%$ will be ready in two weeks. Is there evidence to reject this hypothesis at $\alpha = 0.05 ?$ Ready to pick Ripe Ready in three days Ready in one week Ready in two wet Number of oranges 10 18 14 20

A psychology instructor gave a five-question true-false quiz to her class of 178 students. The results were as follows. Number Correct 0 1 2 3 4 5 Observed 8 30 56 48 26 10 The instructor thinks that the students may have answered the questions by guessing, so tl probability that any given answer is correct is $0.5$ . Under the null hypothesis, the number of correct answers has a binomial distribution with 5 trials and success probability $0.5$ . Perform a chi-square test of this hypothesis. Can you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?

In a goodness of fit test between one observed frequency distribution and one expected frequency distribution, the degrees of freedom are equal to the number of categories minus two.

When data are arranged in table form for the chi-square independence test, it is called a table.

A random group of customers at a fast food chain were asked whether they preferred hamburgers, chicken sandwiches, or fish sandwiches. The restaurant's marketing department claims that $50 \%$ of customers prefer hamburgers, $32 \%$ of the customers prefer chicken sandwiches, and $18 \%$ of the customers prefer fish sandwiches. Is there evidence to reject this hypothesis at $\alpha = 0.05$ ? Plans Hamburgers Chicken Fish Number of students 40 20 6

The number of drunk-driving arrests were counted each month by the Millville po department. The results are given in the following table. Month Number of Drunk-Driving Arrests January 21 February 21 March 13 April 10 May 10 June 10 July 14 August 10 September 11 October 12 November 11 December 29 Test the hypothesis that drunk-driving arrests are equally likely to occur in any mc Use the $\alpha = 0.01$ level of significance.

A random group of used books was selected from book warehouse to analyze their condition. The book store believes that $30 \%$ of the books are in excellent condition, 38 are in very good condition, $19 \%$ are in fair condition, and $13 \%$ are in poor condition. Is there evidence to reject this hypothesis at $\alpha = 0.05$ ? Book condition Excellent Very good Fair Poor Number of oranges 21 28 20 10

A shoe salesman wants to see if his female customers have a preference in the color of sh purchased. Compute the test value for the following data. Black Brown Red Navy White 48 32 13 18 23

The chi-square independence test can be used to test the independence of two variables.