AP Statistics Significance Tests

A company that manufactures laptop batteries claims the mean battery life is 16 hours. Assuming the distribution of battery life is approximately normal, a consumer group will conduct a hypothesis test to investigate whether the battery life is less than 16 hours. The group selected a random sample of 14 of the batteries and found an average life of 15.6 hours with a standard deviation of 0.8 hour. Which of the following is the correct test statistic for the hypothesis test?

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

The campus bookstore at a local university is interested in finding out whether the textbook preference and the class level (freshman, sophomore, junior, senior) of the student are associated. A random sample of 100 students is obtained, and each student in the sample is asked which textbook he or she prefers: new books, used books, or digital books. The students are also asked whether their class level is freshman, sophomore, junior, or senior. Which of the following is the appropriate test for the investigation?

• A one-sample -test for a population mean

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

• A chi-square goodness-of-fit test

• A chi-square test of homogeneity

• A chi-square test of independence

What is another name for the "coefficient of determination?"

• R-Squared Value

• R-Value

• Correlation Coefficient

• Slope

The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes.  What is the probability that a random sample of 40 students will have a mean completion time greater than 25 minutes?

• 0.9678

• 0.0322

• 0.0344

• 0.3851

A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times.  The probability that more than 1/3 of the tosses are heads is closest to 

• 0.9951

• 0.33

• 0.109

• 0.09

The incomes in a certain large population of college teachers have a normal distribution with mean $60,000 and standard deviation $5000.  Four teachers are selected at random from this population to serve on a salary review committee.  What is the probability that their average salary exceeds $65,000?

• 0.0228

• 0.1587

• 0.8413

• 0.9772

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population.  Which of the following would produce a wider confidence interval, based on these same data?

• Use a larger confidence level

• Use a smaller confidence level

• Use the same confidence level, but compute the interval n times.  Approximately 5% of these intervals will be larger

• Increase the sample size