Exam 11: Comparisons Involving Proportions and a Test of Independence

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

Exhibit 11-6 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. -Refer to Exhibit 11-6. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

The sampling distribution for a goodness of fit test is the

Exhibit 11-2 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. -Refer to Exhibit 11-2. The test statistic is

Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With   0.05, test to see if the methods of payment have changed during the Christmas rush.

In a sample of 40 Democrats, 6 opposed the President's foreign policy, while of 50 Republicans, 8 were opposed to his policy. Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Exhibit 11-5 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. -Refer to Exhibit 11-5. The expected number of freshmen is

The test of independence presented in our textbook requires that there be

In a random sample of 200 Republicans, 160 opposed the new tax laws. While in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed as

If a hypothesis is rejected at 95% confidence,

Exhibit 11-3 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. -Refer to Exhibit 11-3. The 95% confidence interval for the difference between the two proportions is

In conducting a hypothesis test about p₁ - p₂, any of the following approaches can be used except

Exhibit 11-6 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. -Refer to Exhibit 11-6. The number of degrees of freedom associated with this problem is

The properties of a multinomial experiment include all of the following except

A movie based on a best-selling novel was recently released. Six hundred viewers of the movie, 235 of whom had previously read the novel, were asked to rate the quality of the movie. The survey showed that 141 of the novel readers gave the movie a rating of excellent, while 248 of the non-readers gave the movie an excellent rating. a. Develop an interval estimate of the difference between the proportions of the two populations, using a .05 level of significance, as the basis for your decision. b. Can we conclude, on the basis of a hypothesis test about p₁ - p₂, that the proportion of the non-readers of the novel who thought the movie was excellent is greater than the proportion of readers of the novel who thought the movie was excellent? Use a .05 level of significance. (Hint: this is a one-tailed test.)

The test statistic for the chi-square tests in our textbook requires, for each category, an expected frequency of at least