Exam 11: Other Chi-Square Tests

A random group of desktop computer sales was selected from an electronic discount chain to analyze the size of monitor purchased with the computer. Is there evidence to reject the hypothesis that the number of monitors is equally distributed between the five types, at $\alpha = 0.05$ ? Monitor type 1 CRT 1 flat panel 1 CRT 1 flat panel 1 Number of sales 13 23 13 10

A biology professor claims that, on the average, $15 \%$ of her students get a grade of A, $25 \%$ get a B, $40 \%$ get a C, $15 \%$ get a D, and $5 \%$ get an F. The grades of a random sample of 115 students were recorded. The following table presents the re Grade 1 2 3 4 5 Observed 28 24 39 17 7 i). Compute the expected frequencies. ii). What is the value of $\chi ^ { 2 }$ ? iii). How many degrees of freedom are there? iv). Test the hypothesis that the grades follow the distribution claimed by the profi Use the $\alpha = 0.01$ level of significance.

Two computer stores recorded the number of computers sold in a week along with the sizes of their hard drives. At $\alpha = 0.05$ , test the claim that the distribution of hard drives at store where the computers were bought are not related. Number of computers 20 GB drive 40 GB drive 80 GB drive 160 GB driv। Store 1 13 11 11 8 Store 2 104 33 15 10

A random group of seniors was selected from a university and asked about their plans for the following year. The school advising office claims that $50 \%$ of the students plan to work, $20 \%$ of the students plan to continue in school, and $30 \%$ of the students plan to take some time off. Is there evidence to reject this hypothesis at $\alpha = 0.05$ ? Plans Work School Time off Number of students 21 13 8

Monica, a chef at a 5 -star restaurant makes eight different desserts. She wants to see if th customers prefer any specific dessert to another. She keeps a record of desserts ordered o course of several weeks, and the results are summarized in the table below. Dessert Frequency Chocolate Mousse 25 Baked Alaska 12 Orange Cheesecake 23 Caramel Flan 32 Banana Brulee 40 Mississippi Mud Pie 20 Ricotta Cannoli 38 French Walnut Torte 34 Find the critical value at $\alpha = 0.05$ .

The chi-square goodness-of-fit test is always one-tailed left.

An anatomy teacher hypothesizes that the final grades in her class are distributed as $10 \%$ A's, $23 \%$ B's, $45 \%$ C's, 14\% D's, and $8 \%$ F's. At the end of the semester, she has the follo grades. A B C D F 6 14 22 8 4 Find the critical value. Use $\alpha = 0.05$ .

The degrees of freedom for a 7×5 contingency table would be 24.

The two types of tests that use a contingency table are the independence test and the test.

A contingency table is made up of 8 rows and 4 columns. How many degrees of freedom are present?

A researcher selected a sample of 50 residents from each of three different cities to determine if they were willing to participate in a medical experiment. At $\alpha = 0.05$ , test the claim that the proportions who will participate are equal. Residents City 1 City 2 City 3 Willing to participate 19 15 22 Not willing to participate 31 35 28 Total 50 50 50

For the given table of observed frequencies, perform a test for independence, using the $\alpha = 0.01$ level of significance. 1 2 3 57 61 64 85 101 90 40 80 84

A biology professor claims that, on the average, $15 \%$ of her students get a grade of A, $25 \%$ get a B, $35 \%$ get a C , $10 \%$ get a D, and $15 \%$ get an F. The grades of a random sample of 119 students were recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 28 11 38 13 29 Compute the expected frequencies.