Understanding Statistical Errors and Confidence Intervals in Research

Question 1 0.7 / 0.7 pts Which of the following is not directly related to the sample size calculations in the case of one sample z testing? a. The set level of confidence b. The margin of error about your estimate c. The population standard deviation d. The upper bound of your confidence interval Question 2 0.7 / 0.7 pts Which of the following would correctly result in a type II error for the Ho that the average age of children with Hodgkin’s lymphoma is 13 years old and the Ha that the average age of children with Hodgkin’s lymphoma is not 13 years old based on the following resulting confidence interval? (13.2, 17.8 years) a. Reject the Ho based on the fact that the Ho value is not within the interval b. Fail to reject the Ho based on the fact that the Ho value lies within the interval c. Fail to reject the Ho based on the fact that the Ho value does not lie within the interval d. Reject the Ho based on the fact that the Ho value lies within the interval

Question 3 0.68 / 0.68 pts Which of the following would incorrectly result in a type I error for the Ho that the average resting heart rate for individuals with pre-hypertension is 71 bpm based on the following confidence interval resulting from the investigation? (70.5, 79.5 beats per minute) a. Reject the Ho based on the fact that the Ho value lies within the interval b. Reject the Ho based on the fact that the Ho value does not lie within the interval c. Fail to reject the Ho based on the fact that the Ho value does not lie within the interval d. Fail to reject the Ho based on the fact that the Ho value lies within the interval Question 4 0.66 / 0.66 pts Which of the following least describes the precision of an estimate? a. The size of the margin of error b. The point estimate itself c. The standard deviation d. The size of the confidence interval

Incorrect Question 5 0 / 0.66 pts Which of the following hypothetical examples would result in the least precise measurement? a. A 95% confidence interval for the average age of a population based on a sample average of 47 years with a population standard deviation of 34 years based on a sample size of 12 individuals. b. A 95% confidence interval for the average age of a population based on a sample average of 52 years with a population standard deviation of 12 years based on a sample size of 87 individuals. c. A 99% confidence interval for the average age of a population based on a sample average of 62 years with a population standard deviation of 22 years based on a sample of 43 individuals. Pg. 224 Question 6 0.66 / 0.66 pts Which of the following hypothetical examples would result in the most precise measurement? a. A “virtually certain” confidence interval (Use Z=3.0) for the average wait times for scheduling an appointment with a primary care physician based on a sample average of 11.4 days with a population standard deviation of 2.3 days based on a sample size of 246 households. b. A 95% confidence interval for the average wait times for scheduling an appointment with a primary care physician based on a sample average of 9.4 days with a population standard deviation of 3.4 days based on a sample size of 73 households.

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c. A 95% confidence interval for the average wait times for scheduling an appointment with a primary care physician based on a sample average of 7.3 days with a population standard deviation of 2.9 days based on a sample size of 81 households. Question 7 0.66 / 0.66 pts Which of the following statements regarding confidence intervals is least accurate? a. As you increase the confidence level α, the precision of your estimate decreases b. As you decrease the confidence level α, the precision of your estimate increases c. Establishing a higher α level controls for nonrandom sources of error due to bias d. Confidence intervals are established to account for random error in sampling Question 8 0.66 / 0.66 pts Which of the following correctly describes the relationship between the standard normal and the t distribution? a. The standard normal is an approximation to the t distribution b. As the degrees of freedom increase, the t distribution approaches the standard normal

c. As the degrees of freedom decrease, the t distribution approaches the standard normal d. The t distribution is the inverse operation of the standard normal Question 9 0.66 / 0.66 pts After conducting a calculation for sample size for a paired t-test procedure, a researcher determines that he needs only 28 participants. Which of the following conclusions should be drawn following this calculation? a. The researcher should pursue enrolling 28 patients in this study b. The researcher should inflate his estimated sample size calculation to above 30 to compensate for the difference between the t and standard normal distributions. c. The researcher should apply an adjustment factor of (df+3)/(df+1) d. The researcher should consider re-evaluating the measurements used in calculation before continuing to enroll Question 10 0.66 / 0.66 pts After conducting a calculation for sample size for a paired t-test procedure, a researcher determines that he needs 40 participants. Which of the following conclusions should be drawn following this calculation? a. The researcher should pursue enrolling 40 patients in this study

b. The researcher should inflate his estimated sample size calculation to above 40 to compensate for the difference between the t and standard normal distributions. c. The researcher should apply an adjustment factor of (df+3)(df+1) d. The researcher should consider re-evaluating the measurements used in calculation before continuing to enroll Question 11 0.66 / 0.66 pts Which of the following is a key difference between the t distribution with degrees of freedom X, and the standard normal? a. The standard normal will always have a higher peak about the mean. b. The t distribution will always have a higher peak about the mean. c. The t distribution typically has a smaller area near the tails of the distribution. d. The t distribution typically has a larger area near the tails of the distribution. Question 12 0.66 / 0.66 pts Which of the following correctly organizes the meaning of the values in Table C of your (pp. 240 of course text regarding the t distribution?

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a. Columns represent the power, Rows represent the degrees of freedom, and cells represent cumulative probabilities b. Columns represent the cumulative probability, Rows represent the alpha levels, and cells represent the degrees of freedom c. Columns represent the cumulative probability, Rows represent the degrees of freedom, and cells represent the values for each percentile d. Columns represent the percentiles, Rows represent the degrees of freedom, and cells represent the cumulative probabilities Question 13 0.66 / 0.66 pts A researcher is interested in the effectiveness of a new program at reducing the average systolic blood pressure in a population with a new anti- hypertensive medication. The researcher wants to test the hypothesis that the mean difference in systolic blood pressure is greater than 40 mmHG. Which of the following represents the correct null and alternative hypotheses for the study? a. Ho: µ1 - µ2 = 0, Ha: µ1 - µ2 = 40 b. Ho: µ1 - µ2 = 40 Ha: µ1 - µ2 ≠ 40 c. Ho: µD = 40 Ha: µD >40 d. Ho: µD = 40 Ha: µD ≠40

Question 14 0.66 / 0.66 pts Suppose researchers are interested in a program that is intended to reduce overall calorie intake in a group of women looking to lose weight after pregnancy. The program manager sets a daily calorie intake limit of 2,050calories/day. Which of the following represents the null and alternative hypotheses representing a two-sided one sample t-test for the average calorie consumption in the weight management program? a. Ho: µ=2,050, Ha: µ<2,050 b. Ho: µ≠2,050, Ha: µ=2,050 c. Ho: µ=2,050, Ha: µ>2,050 d. Ho: µ=2,050, Ha: µ≠2,050 Question 15 0.66 / 0.66 pts Researchers are interested in the effectiveness of a new therapeutic methodology at decreasing performance on the Global Depression Scale (GDS). Suppose clinical relevancy in this field would mandate that the methodology needs to decrease a score on the GDS in a clinically depressed individual by more than 5 points. Which of the following represents the correct null and alternative hypotheses for the t-test that should be implemented in this investigation? a. Ho: µD=0, Ha: µD≠0 b. Ho: µD=5, Ha: µD≠5 c. Ho: µD=5, Ha: µD≤5

d. Ho: µD=5, Ha: µD>5

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Quiz Pubh 6033 module 6

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