23 Foundations Of Statistical inference

Question 1

There are 10 red marbles and 40 blue marbles in a jar. What is the probability that the first marble selected from the jar is a red marble?
a. 0.10
b. 0.20
c. 0.40
d. 1.00

Answer 1

b

Rationale: Probability is the likelihood that any one event will occur given all possible outcomes. In this case the probability that a red marble will be selected from all the marbles is 10 out of 50 (10/50) or 0.20.

Question 2

Sampling error is the difference between the __________ and the ____________.
a. Sample mean; sample standard deviation
b. Population mean; population standard deviation
c. Sample mean; population mean
d. Sample standard deviation; population mean

Answer 2

c

Rationale: Sampling error is the difference between the sample value and the population value. In practice, it is difficult to determine since the population parameter may not be known

Question 3

As sample size increases, the standard error of the mean __________.
a. increases
b. decreases
c. stays the same
d. increases or decreases

Answer 3

b

Rationale: The standard error of the mean decreases when the sample size increases since it is equal to the standard deviation divided by the square root of the sample size.

Question 4

Birthweights are measured for a sample of 20 infants. The 95% confidence interval for this
distribution is 6.2 to 7.4 pounds. Based on this confidence interval which of the following statements
is correct?
a. 95% of all infants will weigh between 6.2 and 7.4 pounds.
b. We are 95% confident that a randomly selected infant will weigh between 6.2 and 7.4 pounds.
c. 95% of the time the mean birth weight of a sample will be 6.8 pounds.
d. We are 95% confident that the population mean for birth weight is between 6.2 and
7.4 pounds.

Answer 4

d

Rationale: A 95% confidenceTinEtSerTvaBlAprNoKviSdeEsLthLeEiRnt.erCvaOlMof which we are 95% confident where the population parameter is located. It does not refer to sample values.

Question 5

The 95% confidence interval for the birthweight of 20 randomly selected infants is given as 6.2 and 7.4 pounds. Based on this confidence interval, which of the following statements is true?
a. The sample mean is 6.8 pounds.
b. We are 95% confident that the mean of the population is 6.8 pounds.
c. We are 95% confident that the sample mean is between 6.2 and 7.4 pounds.
d. The sample mean is unknown.

Answer 5

a

Rationale: The sample mean is the midpoint of a 95% confidence interval for the mean. We are 100% confident that the sample mean is the midpoint of the interval.

Question 6

Compared to the width of a 95% confidence interval, the width of a 99% confidence interval is:
a. Wider
b. Narrower
c. The same
d. Unknown

Answer 6

a

Rationale: In order to increase confidence where the population parameter resides the interval needs to be wider.

Question 7

A researcher believes that an exercise program will be more effective for improving balance than a control activity. The alternative hypothesis (H1) for this study can be written as:
a. c.
b. d.

Answer 7

d

Rationale: Both the null hypothesis and the alternative hypothesis are written in terms of population parameters. The researcher is proposing a directional hypothesis. Therefore, the alternative hypothesis is that the mean will be greater for the experimental group.

Question 8

The calculation of statistical power involves all of the following except:
a. The alpha level of significance
b. The probability level (p)
c. Effect size
d. Number of subjects

Answer 8

b

Rationale: Power analysis involves four interdependent concepts: power, alpha level of significance, the number of subjects, and the effect size. These are known by the mnemonic PANE. Knowing three of the values will allow calculation of the fourth. The p value is a function of the analysis for the data, and does not directly influence power.

Question 9

The critical value for a two-tailed test is _________ than the critical value for a one-tailed test.
a. Smaller c. The same
b. Larger d. Unable to be determined

Answer 9

b

Question 10

All of the following assumptions are important for the use of parametric statistics except:
a. Interval or ratio data
c. Normal distribution of data
b. Variances are homogeneous
d. Random assignment to groups

Answer 10

d

Rationale: Assumptions for parametric tests include interval or ratio data, homogeneity of variances, and normal distribution of data. Random assignment is not a requirement for parametric statistics.

Question 11

Suppose a 95% confidence interval from a study sample for the proportion of Americans who are overweight is 0.29 to 0.37. Which one of the following statements is false?
a. It is reasonable to say that more than 25% of Americans are overweight.
b. It is reasonable to say that more than 40% of Americans are overweight.
c. The hypothesis that 33% of Americans are overweight cannot be rejected.
d. It is reasonable to say that fewer than 40% of Americans are overweight.

Answer 11

b

Rationale: Based on the confidence interval, we are 95% confident that the population parameter is between 0.29 and 0.37 (or 29% to 37%). Therefore, it is reasonable to say that the population value is greater than 25% and less than 40%.

Question 12

In hypothesis testing, a Type II error occurs when:
a. The null hypothesis is not rejected when it is true.
b. The null hypothesis is rejected when it is true.
c. The null hypothesis is not rejected when the alternative hypothesis is true.
d. The null hypothesis is rejected when the alternative hypothesis is true.

Answer 12

a

Rationale: A Type II error is committed when we do not reject the null hypothesis when it is false.

Question 13

Null and alternative hypotheses are statements about:
a. Population parameters.
b. Sample parameters.
c. Sample statistics.
d. It depends - sometimes population parameters and sometimes sample statistics.

Answer 13

a

Rationale: Null and alternative hypotheses should be written in terms of population parameters.

Question 14

A study is done to test the null hypothesis that treatment with drug A is not more effective than drug B for reducing back pain using a VAS. Using  = .05, a statistical test (an independent t-test) found that the difference between the means of the two groups was 6.7, and this was significant at p = .04. Which of the following statements is not a correct interpretation?
a. There is a 4% chance that the groups are not really different.
b. There is a 4% chance that the groups are really different.
c. There is a 4% chance that we would find a difference as big as 6.7 even if the
drugs were not different.
d. If we repeated this study 100 times, we could expect to find 4 studies to show a
significant difference just by chance.

Answer 14

a

Rationale: For p = .04, there is a 4% chance of committing a Type I error, of finding a difference when none exists. The 4% probability does not mean that the groups are different.

Question 15

A test to screen for a serious but curable disease is similar to hypothesis testing, with a null hypothesis of no disease, and an alternative hypothesis of disease. If the null hypothesis is rejected treatment will be given. Otherwise, it will not. Assuming the treatment does not have serious side effects, in this scenario it is better to increase the probability of:
a. Making a Type I error, providing treatment when it is not needed.
b. Making a Type I error, not providing treatment when it is needed.
c. Making a Type II error, providing treatment when it is not needed.
d. Making a Type II error, not providing treatment when it is needed

Answer 15

c

Rationale: Since there are not serious side effects one may err on the side of administering treatment even if it is not needed.

Question 16

All of the following increase the width of a confidence interval except:
a. Increased confidence level c. Increased sample size
b. Increased variability d. Decreased sample size

Answer 16

a

Rationale: There is an inverse relationship between sample size and the width of the confidence interval. Hence increasing sample size will decrease the width of the interval.

Question 17

In hypothesis testing, we use a _________ to make an inference about a _________.
a. sample statistic; population parameter c. population parameter; sample statistic
b. sample statistic; population statistic d. population statistic; sample statistic

Answer 17

d

Rationale: Sample statistics are used to make inferences about population parameters.

Question 18

Power analysis can be used to determine all of the following except:
a. How many subjects are needed to carry out a study.
b. The probability of committing a Type II error.
c. If an effect size is sufficiently large that a statistically a significant result is
probable.
d. If a statistically significant outcome is clinically significant.

Answer 18

d

Rationale: A power analysis can be used to determine sample size based on a given an expected effect size, alpha level and desired power. Only judgment can be used to determine if an outcome has clinical significance.

Question 19

All of the following describe an effect size index except:
a. A standardized ratio that estimates the degree to which the null hypothesis is false. b. A ratio of variance and sample size.
c. A unitless ratio that allows comparison of results across studies.
d. A ratio of the difference between groups and the variance within the groups.

Answer 19

b

Rationale: The effect size index is a ratio of the strength of an effect (difference or relationships) divided by the variance. The null hypothesis indicates an effect size of zero.

Question 20

To plan a study, a researcher must determine how large a sample to recruit. This requires
estimating an effect size that should be achieved. Which of the following is not a strategy for
estimating effect size?
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a. Referring to findings from prior research on similar samples and variables.
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b. Using clinical judgment based on experience with similar patients.
c. Referring to sample sizes used in prior research.
d. Using a conventional effect size.

Answer 20

c

Rationale: Every study is based on different parameters, and other sample sizes may not fit your study. However, all of the other strategies allow the researcher to make a realistic estimate.

Question 21

Two researchers are interested in the effects of drugs on reducing tremor in patients with Parkinson’s disease One researcher designs a study to compare drug A to a placebo, resulting in a significant difference at p =.04. A second researcher designs a study to compare drug B to a placebo, resulting in a significant difference at p =.002. Which of the following statements is correct?
a. Drug B has a stronger effect than Drug A.
b. Drug A has a stronger effect than Drug B.
c. Drug A and Drug B are equally effective.
d. There is no way to know if drug A is better than drug B.

Answer 21

d

Rationale: The p values cannot be used as effect sizes. These decisions will be influenced by sample size, variance in the sample, and many other study design features.

Question 22

A study is designed to estimate the difference in weight loss with two types of diets, A and B. A total of 1000 men who are overweight are recruited, 500 randomly assigned to each type of diet.
The researcher finds that the difference in weight loss between the two groups is 5 pounds at p = .01, and concludes that diet A is better than diet B. Which of the following statements is accurate?
a. The researcher may be committing a Type II error.
b. The significant difference may be due to the sample size.
c. The power of the study was too small to see a bigger effect size.
d. The effect size would be larger if the sample was bigger

Answer 22

b

Rationale: The large sample would increase power substantially, allowing a small effect size to be statistically significant.

Question 23

A researcher designs a study to show that a newly designed spirometer (A) can be substituted for the established model (B) for improving pulmonary function because it is cheaper to manufacture. The null hypothesis for this study would be:
a. There is no significant difference between spirometer A and B.
b. Spirometer A will be more effective than spirometer B.
c. Spirometer B will be more effective than spirometer A.
d. Spirometer A is no worse than spirometer B.

Answer 23

c

Rationale: This is a non-inferiority design, with the intent of showing that the new device is “no worse” than the old one. The null and alternative hypotheses are reversed. Choice D is the alternative hypothesis (the hypothesis we want to accept) . Choice C is the null (the hypothesis we want to reject). We want to reject the statement that the standard device (B) is better than the new device (A). Choice B is not correct because it suggests that A is better than B, which is not the intent of the study. Choice A is a standard null hypothesis, which does not work for a non-inferiority trial.