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Statistical Methods and Hypothesis Testing: Practice Questions and Solutions

Practice exercises on hypothesis testing, probability, and data interpretation.

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    Statistical Methods and Hypothesis Testing: Practice Questions and Solutions 1. In a statistical study the population is A) the group of people from which the sample is taken B) all of the people in the United States C) all of the people in the world D) the people who comprise the sample Feedback: The population is the larger group of people from which the sample was taken Points Earned: 0.0/1.0 Correct Answer(s): A 2. The sample mean is an estimate of: A) The average value for people NOT in the population B) The average value in the sample C) The true population mean Feedback: The sample mean is an estimate of the true population mean. It is, however, an exact measurement of the average value in the sample since the sample data is what is used to calculate the sample mean. Points Earned: 0.0/1.0 Correct Answer(s): C 3. A summary measure calculated from the sample is called a(n): A) parameter B) statistic C) outlier Feedback: Sample measures are statistics; population measures are parameters Points Earned: 1.0/1.0 Correct Answer(s): B

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    4. Which of the following is a parameter? A) mu B) x - bar C) p - hat D) Z Feedback: x - bar and p - hat are sample statistics while Z is a test statistic. Points Earned: 0.0/1.0 Correct Answer(s): A 5. Which of the following is an example of paired data? A) The average time to cook the same meal is compared for men and women. B) The proportion of children that get a cold in Winter in Pittsburgh is compared to the proportion of children that get a colding in Winter in Dallas. C) A researcher wants to test the time it takes to send a text message for adults and children. D) Data measured to compare handwriting between the left and right hands of 30 subjects. Feedback: Handwriting between left and right hands is paired data since it is repeated measurements on the same subject. Points Earned: 0.0/1.0 Correct Answer(s): D 6. In a poll of n = 100 randomly selected individuals, 25 people said they are opposed to the death penalty for persons convicted of murder. Which expression above correctly shows the calculation of the standard deviation of the sample proportion? A) Expression A B) Expression B

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    C) Expression C Feedback: The standard error is found by taking the square root of (0.25)*(0.75)/100 = 0.0433 Points Earned: 1.0/1.0 Correct Answer(s): A 7. From a random sample of 20 women from a women’s only health club, 60%, or 12, stated that they wished the club would stay open longer. Which of the following best defines what this 60% represents? A) population B) statistic C) parameter D) sample Feedback: Because this value came from a sample the 60% defines a statistic. Points Earned: 0.0/1.0 Correct Answer(s): B 8. Suppose that 200 different polling organizations and academic researchers all do surveys in which the same question is asked. All 200 research groups construct a 90% confidence interval for the proportion who would say "yes" to this question. About how many of the 200 different 90% confidence intervals will capture the value of the population proportion? A) 90 B) 95 C) 180 D) 190 Feedback: Simply, you would expect to be "correct" 90 percent of the time. So 90 percent of 200 is 180. Points Earned: 1.0/1.0 Correct Answer(s): C 9.

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    In a poll of n = 200 randomly selected individuals, 50 people said they are opposed to the death penalty for persons convicted of murder. Which choice from the display above correctly shows the calculation for a 90% confidence interval for the population proportion opposed to the death penalty? A) Equation A B) Equation B C) Equation C D) Equation D Feedback: With a sample proportion of 50 out or 200 or 0.25 the correct equation would be 0.25 ± the square root of [(0.25)*(1 − 0.25) divided by 200]. Points Earned: 1.0/1.0 Correct Answer(s): D 10. Based on the output above, what is the Standard Error of the mean? A) 1.60 B) 2.4 C) 12.0 D) 23.8 Feedback: The standard error of the mean is found by taking the sample standard deviation, 60, and dividing by the square root of the sample size, which is 5. This results in a standard error of 12.0 Points Earned: 1.0/1.0 Correct Answer(s): C

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    11. Suppose a 95% confidence interval for the proportion of Americans who exercise regularly is 0.29 to 0.37. Which one of the following statements is NOT true? A) It is reasonable to say that more than 25% of Americans exercise regularly. B) It is reasonable to say that more than 40% of Americans exercise regularly. C) An "acceptable" hypothesis is that about 33% of Americans exercise regularly. D) It is reasonable to say that fewer than 40% of Americans exercise regularly. Feedback: All are reasonable except to say that more than 40% of Americans exercise regularly. This is because the confidence interval is less than 40%. Points Earned: 1.0/1.0 Correct Answer(s): B 12. For which of the following situations would the Central Limit Theorem for sample means NOT apply? A) A random sample of size 20 is drawn from a skewed population. B) A random sample of size 50 is drawn from a skewed population. C) A random sample of size 20 is drawn from a normal population. D) A random sample of size 50 is drawn from a normal population. Feedback: For sample sizes of 30 or more the Central Limit Theorem states that even for a skewed population the sample mean distribution will approximated a normal distribution, and if the population is bell - shaped then so to will the distribution of the sample means regardless of sample size. Thus the response that does not follow the Rules is the one of sample size of 20 from a skewed distribution Points Earned: 1.0/1.0 Correct Answer(s): A 13. A 95% confidence interval for the proportion of women that has ever dozed off while driving is 0.07 to 0.14. For men, a 95% confidence interval for the proportion that has ever dozed off while driving is 0.19 to 0.25. Assume both intervals were computed using large random samples. What conclusion can be made about the population proportions that have dozed off while driving? A) It is reasonable to conclude that there is a difference between men and women. B) It is not reasonable to conclude that there is a difference between men and women. C) It is reasonable to conclude that there is a difference of .05 between men and women. D) No conclusion is possible because we don’t know the margin of error. Feedback: The intervals do not overlap indicating that a statistically significant difference exists. Points Earned: 1.0/1.0

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