AP Statistics Tests of Significance

Given the regression analysis, what is the equation of the LSRL?

• y(hat)=38257x-0.163

• y(hat)=38257-0.163x

• y(hat)=2446-0.163x

• y(hat)=2446x-0.163

Researchers are testing a new diagnostic tool designed to identify a certain condition. The null hypothesis of the significance test is that the diagnostic tool is NOT effective in detecting the condition. For the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. Which of the following should the researchers do to avoid the more consequential error?

• Increase the significance level to increase the probability of Type I error

• Increase the significance level to decrease the probability of Type I error.

• Decrease the significance level to increase the probability of Type I error

• Decrease the significance level to decrease the probability of Type I error.

A random sample of 240 adults over the age of 40 found that 144 would use an online dating service. Another random sample of 234 adults age 40 and under showed that 131 would use an online dating service. Assuming all conditions are met, which of the following is the standard error for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service?

A study reports that 75 percent of young adults in a county get their news from online sources. A sociologist believes that the percentage is actually greater than 75 percent. The sociologist will select a random sample of young adults from around the county to interview. Which of the following is the most appropriate method for investigating the sociologist’s belief?

• A one-sample -test for a difference in population proportions

• A one-sample -test for a sample proportion

• A one-sample -test for a population proportion

• A two-sample -test for a difference in population proportions

• A two-sample -test for a difference in sample proportions

A marketing executive is investigating whether this year’s advertising campaign has resulted in greater mean sales compared with last year’s mean sales. The executive collects a random sample of 100 customer orders from a large population of orders and calculates the sample mean and sample standard deviation. Which of the following is the appropriate test for the executive’s investigation?

• A one-sample -test for a population mean

• A one-sample -test for a population mean

• A one-sample -test for a population proportion

• A two-sample -test for a difference between means

• A matched-pairs -test for a mean difference

Milk has a PH of 6.7, which is slightly acidic. Cheese makers add a culture to milk to lower the PH, making it more acidic and turning it into cheese. A manufacturer is experimenting with a new culture that claims to produce a PH of 5.2, which is perfect for cheddar cheese. A set of 50 test batches resulted in an average PH of 5.11. A one sample -test was conducted to investigate whether there is evidence that the mean PH is different from 5.2. The test resulted in a PH-value of 0.018. Which of the following is a correct interpretation of the -value?

• The probability that the true PH is equal to 5.2 is 0.018.

• The probability that the true PH is different from 5.2 is 0.018.

• The probability of observing a sample mean of 5.11 or less is 0.018 if the true mean is 5.2.

• The probability of observing a sample mean of 5.11 or more is 0.018 if the true mean is 5.2.

• The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the true mean is 5.2.

A company director investigated whether there is a difference in the mean number of overtime hours worked each

week by employees assigned to two different managers. Each manager, A and B, manages 100 employees. Random

samples of 35 employees from manager A and 40 employees from manager B were selected. The number of

overtime hours worked was recorded for the 75 employees each week. Have the conditions been met for inference with a confidence interval for the difference in the population means?

• Yes, all conditions have been met.

• No, because the data were not collected using a random method.

• No, because the size of at least one of the samples is greater than 10 percent of the population.

• No, because the sample sizes are not large enough to assume the distribution of the difference in sample

  means is normal.

• No, because the sample sizes are not the same.

A study was conducted to investigate whether there are regional differences in peanut butter preference in the United States. The country was divided into 7 geographic regions, and in each region a random sample of peanut butter eaters were asked whether they preferred creamy or crunchy peanut butter. The responses were summarized in a 7-by-2 table of counts for each combination of geographic region and creamy or crunchy peanut butter preference. Which of the following tests is the most appropriate for the investigation?

• A two-sample -test for a difference between means

• A two-sample -test for a difference between proportions

• A chi-square test of homogeneity

• A chi-square test of independence

• A chi-square goodness-of-fit test

Interpret the coefficient of determination from the computer output seen here:

• As the price increases, the miles driven go up by about 66.4%

• As the miles driven increase, the price increases by about 66.4%.

• About 66.4% of the variability in miles driven is accounted for by the LSRL.

• About 66.4% of the variability in price is accounted for by the LSRL.

A friend has placed a large number of plastic disks in a hat and invited you to select one at random.  He informs you that half are red and half are blue.  If you draw a disk, record the color, replace it, and repeat 100 times, which of the following is true?

• It is unlikely you will choose red more than 50 times.

• If you draw 10 blue disks in a row, it is more likely you will draw a red on the next try.

• The overall proportion of red disks drawn should be close to 0.50.

• The chance that the 100th draw will be red depends on the results of the first 99 draws.