Exam 14: Analysis of Categorical Data

A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 80% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 65 plants had red petals. Use the chi-square goodness-of-fit test to determine whether the sample data confirm the geneticist's prediction. Find the approximate p-value and use it to make your decision. Compute : ______________ Reject when > ______________. The p-value ______________. We have sufficient evidence to conclude that the geneticist's model ______________ correct. Use the large-sample z-test to test the hypothesis H₀: p = 0.80. Compute the z-statistic. ______________ The p-value ______________. We have sufficient evidence to conclude that the geneticist's model ______________ correct.

The middle 0.95 portion of the chi-square distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.

A right-tailed area in the chi-square distribution equals 0.05. For 6 degrees of freedom the table value equals 12.5916.

Researchers from Germany claimed that the risk of a heart attack for a working person may be as much as 50% greater on Monday than on any other day. In an attempt to verify their claim, they surveyed 420 working people who had recently had heart attacks and recorded the day on which their heart attacks occurred: Do the data present sufficient evidence to indicate that there is a difference in the incidence of heart attacks depending on the day of the week? Test using = 0.05. Compute : ______________ Reject when > ______________. Conclude that there is ______________ evidence to indicate a difference in frequency of occurrence of a heart attack from day to day.

In chi-square tests, there is a rule known as Rule of Five, which requires that:

A take-out pizza palace offers four different pizzas. The manager believes that 45% of the single pizza customers prefer pepperoni pizza, 35% prefer the combination pizza, 15% prefer the taco pizza and 5% prefer the vegetarian pizza. To check his belief, the manager takes a random sample of 100 single pizza orders and records the following information: Do the sample data present sufficient evidence to support the manager's belief? Test the appropriate hypotheses at the 10% significance level. Compute : ______________ Thus, one should ______________ . Conclude that the current data ______________ the manager's belief.

Whenever the expected frequency of a cell is less than 5, one remedy for this condition is to decrease the size of the sample.

A national survey stated that 30% of the population prefers to use a pen with black ink, 30% prefer blue ink, 25% prefer red ink and 15% prefer some other color. A statistics professor took a random sample of 80 students and asked them to state their ink color preference. The following data was recorded: Test whether the data agrees with the percentages stated in the national survey. Compute the value of the test statistic. What is ? ______________ Set up the appropriate rejection region for = 0.05 Reject when > ______________. What is the appropriate conclusion? We conclude that the data ______________ with the national survey.

A contingency table test with 4 rows and 30 degrees of freedom implies that the table must have:

A multinomial experiment, where the outcome of each trial can be classified into one of two categories, is identical to the binomial experiment.

When the expected cell frequencies are smaller than 5, the cells should be combined in a meaningful way such that the expected cell frequencies do exceed 5.

Which of the following statements about a goodness-of-fit test is false?

A survey of 500 respondents produced these cell counts in a 2 3 contingency table: If you wish to test the null hypothesis of "independence" - that the probability that a response falls in any one row is independent of the column it falls in - and you plan to use a chi-square test, how many degrees of freedom will be associated with the statistic? df = ______________ Compute : = ______________ Reject when > ______________. Conclude that there ______________ reason to expect a dependence between rows and columns. Find the approximate p-value for the test. The p-value ______________ .10

If we wish to determine whether there is evidence that the proportion of successes is the same in group 1 as in group 2, the appropriate test to use is:

A large carpet store wishes to determine if the brand of carpet purchased is related to the purchaser's family income. As a sampling frame, they mailed a survey to people who have a store credit card. Five hundred customers returned the survey and the results follow: At the 5% level of significance, can you conclude that the brand of carpet purchased is related to the purchaser's family income? Test statistic = ______________ Critical Value = ______________ Conclusion: ______________ We can conclude that the brand of carpet purchased ______________ related to the purchaser's family income.

A chi-square test for independence with 6 degrees of freedom results in a test statistic of 13.25. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that p-value is greater than 0.025 but smaller than 0.05.

Consider a multinomial experiment with 200 trials, and the outcome of each trial can be classified into one of 5 categories. The number of degrees of freedom associated with the chi-square goodness-of-fit test equals:

All chi-square distributions are skewed to the right and their means equal the associated degrees of freedom.

To determine whether a single coin is fair, the coin was tossed 250 times, and heads was observed 140 times. The value of the test statistic is:

An experiment was conducted to investigate the effect of general hospital experience on the attitudes of physicians toward lower-class people. A random sample of 50 physicians who had just completed 4 weeks of service in a general hospital were categorized according to their concern for lower-class people before and after their general hospital experience. The data are shown in the table. Do the data provide sufficient evidence to indicate a change in "concern" after the general hospital experience? Compute = ______________ Give a range for the p-value. ______________ Conclude that there is ______________ enough evidence to indicate a change in concern due to the general hospital experience.