Units 5-8 MC Review

A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?

• The bank should not use the data from this survey because this is an observational study.

• The bank can use the result of this survey to prove that working for the bank causes employees to participate in volunteer activities.

• The bank did not select a random sample of employees, so the survey will not provide the bank with useful information.

• The bank would have to use the survey data to construct a confidence interval in order to estimate the proportion of employees who participate in volunteer activities.

• The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.

Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence?

• 80.0%

• 90.0%

• 95.0%

• 95.5%

• 99.0%

A large-sample 98 percent confidence interval for the proportion of hotel reservations that are canceled on the intended arrival day is (0.048, 0.112). What is the point estimate for the proportion of hotel reservations that are canceled on the intended arrival day from which this interval was constructed?

• 0.032

• 0.064

• 0.080

• 0.160

• It cannot be determined from the information given.

When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that

• the sample size is large enough

• the central limit theorem is applicable for the sample mean

• the sample standard deviation is a good approximation of the population standard deviation

• the degree of dependence among observations is negligible

• the sampling method is not biased

A random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours of sleep per day of (6.73, 7.67). Which of the following statements best summarizes the meaning of this confidence interval?

• About 95% of all random samples of 50 students from this population would result in a 95% confidence interval of (6.73, 7.67).

• About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.

• 95% of the students in the survey reported sleeping between 6.73 and 7.67 hours per day.

• 95% of the students in this high school sleep between 6.73 and 7.67 hours per day.

• A student selected at random from this population sleeps between 6.73 and 7.67 hours per day for 95% of the time.

A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95% confidence interval for the proportion of the population of voters who are in favor of the bond issues is

In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet. A broadband company believes that the percent is greater now than it was in 2009 and will conduct a survey. The company plans to construct a 98 percent confidence interval to estimate the current percent and wants the margin of error to be no more than 2.5 percentage points. Assuming that at least 79 percent of adults use the Internet, which of the following should be used to find the sample size (n) needed?

A manufacturer claims its Brand A battery lasts longer than its competitor’s Brand B battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table.

Provided that the assumptions for inference are met, which of the following tests should be conducted to determine if Brand A batteries do, in fact, last longer than Brand B batteries?

• A one-sided, paired t-test

• A one-sided, two-sample t-test

• A two-sided, two-sample t-test

• A one-sided, two-sample z-test

• A two-sided, two-sample z-test

An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had conducted a one-tailed test on the same set of data, which of the following is true about the possible p-value(s) that the experimenter could have obtained?

• The only possible p-value is 0.22.

• The only possible p-value is 0.44.

• The only possible p-value is 0.88.

• The possible p-values are 0.22 and 0.78.

• The possible p-values are 0.22 and 0.88.

A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown.

Which of the following statements best describes the conclusion that can be drawn from this experiment?

• There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).

• There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).

• There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).

• There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

• There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).