Exam 14: Tests of Hypotheses Based on Count Data

An office worker claims that at most $30 \%$ of the phone calls he makes are the nonbusiness type. Test the null hypothesis that $p=0.30$ against a one-tailed alternative if a random sample of 13 of his calls reveals 8 nonbusiness calls. Use $\alpha=0.05$ .

A television station wants to determine if there is a difference in the proportions of people who watched two of their programs. In random samples of 60 and 80 people, 25 and 40 people watched the first and second programs respectively. -Using a 5\% significance level, conduct the test for the situation above.

Ninety out of 120 house-husbands prefer detergent $A$ . If the 90 house-husbands represent a random sample from a population of all potential purchasers, estimate the fraction of total house-husbands favoring detergent $A$ by constructing a $98 \%$ confidence interval.

A manufacturer has test-marketed a new men's cologne. Simple random samples of male students at a university were asked to try the product for four weeks and then were asked the question: "Would you purchase the product?" The results are shown in the following table: -Would you conclude the respondents' preferences are independent of year in college? Conduct the test at $\alpha=0.05$ .

The standard error of the proportion is given by __________.

The chi-square test can be used to determine if there is a significant difference between two sample proportions.

Which of the following conclusions is reasonable for a test of independence at $\alpha=0.05$ if $\mathrm{X}_{0.05}^{2}=18.31$ ?

To decide whether or not observed differences among three sample proportions can be attributed to chance requires the use of the normal distribution table.

An auditor is assigned to investigate the probability of a bank's accounts having errors. If she has reason to believe that the probability is anywhere between 0.15 and 0.40 , how large a sample will she need to be $99 \%$ confident that the estimated percentage of accounts containing errors is within 0.02 of the true percentage?

The null hypothesis that two processes produce the same proportion of defectives can be written

An automobile repair service asks 170 customers with annual incomes under \$20,000, 180 customers with annual incomes from $\$ 20,000$ to $\$ 50,000$ and 150 customers with annual incomes over $\$ 50,000$ whether they rated the repair service as outstanding, above average, average, below average, or poor. What hypotheses do we want to test if we are going to perform a chi-square analysis of the resulting $5 \times 3$ table?

For a contingency table, which of the following is true?

The null hypothesis in a goodness-of-fit test is that the distribution of the sample does not fit the theoretical distribution.

A television station wants to determine if there is a difference in the proportions of people who watched two of their programs. In random samples of 60 and 80 people, 25 and 40 people watched the first and second programs respectively. -In the situation above, suppose the station wants to know if fewer people watched the first program than the second. Use the same sample results and conduct the one-tailed test at $\alpha=0.05$ .

The larger the statistic in a goodness-of-fit test, the __________ likely the data fits the hypothesized distribution.

An office worker claims that at most $30 \%$ of the phone calls he makes are the nonbusiness type. Test the null hypothesis that $p=0.30$ against a one-tailed alternative if a random sample of 13 of his calls reveals 8 nonbusiness calls. Use $\alpha=0.01$ .

To determine if a set of data fits the pattern of the binomial distribution, the __________ test is used.

A placement office at a large university claims that approximately $70 \%$ of the school's graduates will obtain jobs in their major field upon graduation. The administration feels that the percentage is larger than $70 \%$ . From a random sample of 100 recent graduates it was found that 75 had obtained jobs in their field. The hypotheses are

The sample value $\frac{x_{1}}{n_{1}}-\frac{x_{2}}{n_{2}}$ is an estimate of the population value __________.

It is claimed that $40 \%$ of all shoppers at a shopping mall enter a particular department store. A random sample of 14 shoppers at the mall was selected. If the null hypothesis $p=0.40$ is tested against the alternative that $p<0.40$ , the null hypothesis will be rejected at $\alpha=0.01$ if __________ of the 14 shoppers enter the store.