Exam 11: Other Chi-Square Tests

Two allergists recorded the main area of allergy for new patients during a month. At $\alpha = 0.05$ , test the claim that the allergy diagnosis and the doctor that treated the patients at independent. Allergies Pollen Food Mold Pets Doctor 1 7 7 8 8 Doctor 2 26 7 10 24

A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at $\alpha = 0.05 ?$ Year in school Freshman Sophomore Junior Senior Number of students 12 12 13 23

The computational procedure for the homogeneity of proportions differs from that of the test of independence in that it takes into account the standard deviation.

The formula for finding the chi-square test value is .

The following table presents the numbers of cucumber seeds, by brand, that germi failed to germinate 14 days after planting. Brand A Brand B Brand C Brand D Germinated 40 37 41 42 Failed to Germinate 17 14 15 7 Can you conclude that the the germination rate is related to the brand of seed? Usi $\alpha = 0.01$ level of significance.

A biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. The table lists the results of the study. At $\alpha = 0.05$ , test the claim that the rodent type and the success of finishing the maze are nc related. Mice Rats Finished 22 28 Did not Finish 30 11

The method that uses the formula $\chi ^ { 2 } = \sum \frac { ( | O - E | - 0.5 ) ^ { 2 } } { E }$ is called the________ correction for continuity.

A contingency table has 5 rows and 4 columns. How many degrees of freedom are there?

A study was performed at a university to analyze whether the preference for hamburgers or fried chicken is related to the gender of the student. This table lists the results of the study. At $\alpha = 0.05$ , test the claim that the meal preference and the gender of the student a related. Hamburgers Fried Chicken Female 11 26 Male 15 20

If the null hypothesis is not rejected, it can be assumed the proportions are 67) and the differences in them are due to chance.

An assumption for the goodness-of-fit test is that the frequency for each category must be five or more.

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 , $10 \%$ get a D, and $10 \%$ get an $\mathrm { F }$ . The grades of a random sample of 131 students were recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 13 21 73 11 13 What is the value of $\chi ^ { 2 }$ ?

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2$ , $p _ { 3 } = 0.15 , p 4 = 0.15 , p _ { 5 } = 0.15$ . Category 1 2 3 4 5 Observed 38 26 22 4 16 Compute the value of $\chi ^ { 2 }$ .

A product testing laboratory selected a sample of 20 printers from 2 different manufacturers to determine if they could print more than 100,000 pages without breaking down. At $\alpha = 0.05$ , test the claim that the proportions lasting more than 100,000 pages are equal. Manufacturer 1 Manufacturer 2 Lasted past 100,000 14 7 Did not last to 100,000 6 13 Total 20 20

In a chi-square goodness-of-fit test when there is close agreement between the observed frequency and the expected frequency, the chi-square test value will be small.

A quality control supervisor selected a sample of 100 electronic components from each of three different production chains to determine if the production chains had the same rates of meeting their quality standards. At $\alpha = 0.05$ , test the claim that the proportions ar equal. Components Chain 1 Chain 2 Chain 3 Meets the standard 80 87 74 Does not meet the standard 20 13 26 Total 100 100 100

The chi-square distribution is continuous, whereas the goodness-of-fit test is .

A research firm reported that 15% of those surveyed described their health as poor, 26% as good, 40% as very good, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their health. In a sample of 610 people in Chicago, 70 described their health as poor, 180 as good, 220 as very good, and 140 as excellent. Compute the test value.

$\text { The null hypothesis should not be rejected for the data given in the figure below. }$

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.25$ , $p _ { 3 } = 0.1 , p _ { 4 } = 0.1 , p _ { 5 } = 0.2$ . Category 1 2 3 4 5 Observed 43 20 10 4 31 Compute the expected frequencies.