Exam 11: Other Chi-Square Tests

The following table presents the numbers of customers who - after 2 weeks of use satisfied or dissatisfied with their newly-purchased computers. Brand A Brand B Brand C Brand D Satisfied 40 36 29 34 Dissatisfied 11 16 11 7 Can you conclude that the the satisfaction rate is related to the brand of computer? the $\alpha = 0.05$ level of significance.

The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair. At $\alpha = 0.05$ , test the claim that the section of participation and the high school where the students were from are independen Number of Students High School 1 High School 2 High School 3 Mathematics 7 7 18 Physics 37 17 21

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.3$ , $p _ { 3 } = 0.1 , p _ { 4 } = 0.15 , p _ { 5 } = 0.1$ . Category 1 2 3 4 5 Observed 51 32 11 13 16 Test the hypothesis that the distribution of the observed frequencies is as given by the nul hypothesis. Use the $\alpha = 0.01$ level of significance.

$\text { For four degrees of freedom, the value of } \alpha \text { shown in the } \chi ^ { 2 } \text { distribution below is } 0.05 \text {. }$

A chewing gum manufacturer wishes to determine if his customers prefer one flavor gum other flavor. He selects a random sample of customers and records the flavor of gum that purchased. Compute the test value for the data given. Type Number Sold Spearmint 25 Wintergreen 32 Cherry 18 Cinnamon 43

A sample of 141 university students who recently moved off-campus were polled whether they agree that off-campus living is preferable to on-campus living. In adi each was asked how many people live in their current off-campus residence. The 1 are summarized in the following contingency table. 1 2 3 Agree 15 16 34 No Opinion 9 7 17 Disagree 24 9 10 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. Whi do you conclude?

A sociologist wanted to determine whether there was a difference in the amount of time children aged 5-7 spent watching television each day. Check the following data for evidence that the number of minutes spent watching television is equally distributed throughout the week. Use $\alpha = 0.01$ . Day Number of Minutes Sunday 200 Monday 112 Tuesday 123 Wednesday 130 Thursday 160 Friday 225 Saturday 247 Compute the test value.

Find the area to the right of 5.578 under the chi-square distribution with 11 degrees of freedom.

The test of independence of variables is used to determine whether two variables are independent or related when a single sample is selected.

A psychology instructor gave a five-question true-false quiz to her class of 188 students. The results were as follows. Number Correct 0 1 2 3 4 5 Observed 4 27 55 71 27 4 The instructor thinks that the students may have answered the questions by guessi that the probability that any given answer is correct is $0.5$ . Under the null hypothe 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 $\alpha = 0.05$ leve

A sociologist wanted to determine whether there was a difference in the amount of time children aged 5-7 spent watching television each day. Check the following data for evidence that the number of minutes spent watching television is equally distributed throughout the week. Use $\alpha = 0.01$ . Day Number of Minutes Sunday 200 Monday 112 Tuesday 123 Wednesday 130 Thursday 160 Friday 225 Saturday 247 Find the critical value.

A random group of apartments was selected from a city to analyze the number of bedrooms they have. Is there evidence to reject the hypothesis that the apartments are equally distributed between 1 -bedroom, 2-bedroom, and 3-bedroom apartments, at $\alpha = 0.05 ?$ Year in school 1 bedroom 2 bedrooms 3 bedrooms Number of students 8 9 15

The number of visits to a certain web site were counted each day of a particular week. Thi are given in the following table. Day Number of Visits Sunday 144 Monday 103 Tuesday 136 Wednesday 124 Thursday 127 Friday 145 Saturday 156 Test the hypothesis that web site visits are equally likely to occur on any day of the week. $\alpha = 0.05$ level of significance.

A marketing company selected a sample of 25 lawyers and 25 doctors to determine if they had voted in the last election. At $\alpha = 0.05$ , test the claim that the proportions who vo are equal. Lawyers Doctors Voted 17 12 Did not vote 8 13 Total 25 25

A sample of 157 university students who recently moved off-campus were polled to see u they agree that off-campus living is preferable to on-campus living. In addition, each was how many people live in their current off-campus residence. The results are summarized $\mathrm { j }$ following contingency table. 1 2 3 Agree 39 27 29 No Opinion 15 5 7 Disagree 25 6 4 Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?

The table lists the sugar content of two types of apples from three different orchards. At $\alpha = 0.05$ , test the claim that the sugar content of the apples and the orchard where they we grown are not related. Sugar Content Orchard 1 Orchard 2 Orchard 3 Apple Type 1 4 3 7 Apple Type 2 31 9 19

Given that a contingency table has dimensions of $5 \times 5$ , what is the critical value of chi-square at $\alpha = 0.05$ ?

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 Frequenc 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 Compute the test value.

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35$ , $p _ { 2 } = 0.25 , p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.15$ . Category 1 2 3 4 5 Observed 38 31 24 23 4 i). Compute the expected frequencies. ii). Compute the value of $\chi ^ { 2 }$ . iii). How many degrees of freedom are there? iv). Test the hypothesis that the distribution of the observed frequencies is as giver null hypothesis. Use the $\alpha = 0.05$ level of significance.

A four-year university has decided to implement a new approach to teaching Statistics. Full-time and adjunct professors were surveyed to determine whether they preferred the traditional lecture approach or a computer approach to teaching Statistics. Prefer Lecture Prefer Computer No Preference Full-time 8 13 6 Adjunct 11 22 10 Compute the test value.