Question 1

The symbol σ (the lower case Greek letter sigma) is usually used in statistics to refer to the:

Accepted Answer

The symbol σ typically refers to the population standard deviation in statistics. The sample variance is typically represented by s^2, the population mean by μ, and the sample mean by x̄.

Question 2

The population mean is often shown with the lowercase Greek letter:

Accepted Answer

The population mean is typically denoted by the lowercase Greek letter mu (μ).

Question 3

Which of the following will increase the width of the confidence interval?

Accepted Answer

C

Question 4

Statisticians often construct an interval around their point estimates. There are a few ways this can be done. The most common way is called:

Accepted Answer

Confidence intervals are the most common way for statisticians to construct an interval around their point estimates. This provides a range of plausible values for the population parameter with a certain level of confidence.

Question 5

Suppose you conducted a study comparing the means of two groups. You conduct a group t-test and observed p < .05. You can conclude:

Accepted Answer

A significant difference between the means suggests that one group had a higher mean than the other. However, we cannot conclude whether the study worked or failed based solely on the significance level. Additionally, we cannot determine the size of the difference between the means from the significance level alone.

Question 6

Which of the following is an often used formula for the standard error of the mean?

Accepted Answer

The standard error of the mean is calculated by dividing the standard deviation of the population by the square root of the sample size. Therefore, the formula is (standard deviation)/(square root of sample size).

Question 7

One method to calculate a 95% confidence interval is: to sample, with replacement, from the original variable and calculate the statistic; to repeat this thousands of times; and to take the middle 95% of these replicate statistics. This is called:

Accepted Answer

The method described is known as bootstrapping, which is a non-parametric resampling technique used to estimate the sampling distribution of an estimator. It allows for the calculation of confidence intervals without making assumptions about the population distribution or the underlying sampling distribution. ANOVA is a parametric statistical technique used to test differences among means, correlation measures the strength of a linear relationship between two variables, and Efronian super-inference is not a commonly used statistical term.

Question 8

You have collected data from 16 people on a health anxiety scale. The mean is 100 and the standard deviation is 40. What is the 95% confidence interval (to two decimal places):

Accepted Answer

Using the formula for a 95% confidence interval, CI = X̄ ± 1.96 × (s/√n), where X̄ is the sample mean, s is the sample standard deviation, and n is the sample size, we get: 
CI = 100 ± 1.96 × (40/√16) 
CI = 100 ± 1.96 × 10 
CI = (78.69, 121.31) 
Therefore, the best answer choice is B.

Question 9

If you are testing a null hypothesis, and incorrectly fail to reject it, when it is false, this is called an error of the:

Accepted Answer

Failing to reject a false null hypothesis is known as a Type 2 error.

Question 10

The statistical concept of power is most appropriately described as:

Accepted Answer

Power is the probability of correctly rejecting a false null hypothesis. In other words, it is the likelihood of detecting a true effect when there is one. Therefore, option A is the most appropriate description of power. Option B is incorrect because power is only concerned with the rejection of false null hypotheses, not every null hypothesis. Option C is incorrect because it refers to the concept of Type II error (false negative), which is related to power but not the same thing. Option D is incorrect because it refers to effect size, which is related to power but not the same thing.

Question 11

You have conducted a t-test. The result is: t(37) = 2.46, p = .02. What can you conclude?

Accepted Answer

The t-test result provides evidence against the null hypothesis that the effect in the population is zero (which is equivalent to saying that there is no difference between the two groups being compared). The p-value of .02 suggests that this evidence is statistically significant, meaning that it is unlikely to have occurred by chance. Therefore, we can conclude that there is a statistically significant effect (i.e. difference) between the two groups being compared.

Question 12

Which of the following is a common formula for the one-sample t-test?

Accepted Answer

The one-sample t-test formula is typically represented as the difference between the sample mean and the population mean (or a hypothesized value) divided by the standard error of the mean. This is most closely matched by option B, which simplifies to mean/standard error, capturing the essence of comparing a sample statistic to a hypothesized population parameter relative to the variability of the sample.

Question 13

Which of the following is a reason that you might choose to do a Mann-Whitney test rather than a t-test?

Accepted Answer

Mann-Whitney test is a non-parametric test that does not rely on the assumption of normal distribution, making it a good choice when the data's normality is in question.

Question 14

Suppose that you have collected data from two groups of people and want to compare the means of these. Which of the following tests is most appropriate (assuming the data meet assumptions)?

Accepted Answer

A group t-test is the most appropriate test for comparing the means of two independent groups of data. A paired t-test is used for comparing mean differences within the same group, χ2 test for testing the association between two categorical variables, and correlation for testing the relationship between two continuous variables.

Question 15

You are reading an article where the author allocated people to groups and compared means with a Oneway ANOVA. The author reports: F(3,36) = 6.23, p = .05. How many groups did the study have, and how many participants in total?

Accepted Answer

The notation F(3,36) in a one-way ANOVA result indicates that there are 3 degrees of freedom between groups, which corresponds to 4 groups (since degrees of freedom are calculated as the number of groups minus 1), and 36 degrees of freedom within groups, which corresponds to the total number of participants minus the number of groups (40 participants - 4 groups = 36). Therefore, there were 4 groups and 40 participants in total.

Question 16

An odds ratio is used:

Accepted Answer

An odds ratio is a statistic that quantifies the strength of the association between two binary variables, often used in case-control studies.

Question 17

You have conducted a study to examine the association between math scores and generalized anxiety. Your result is: r = .11, n=1,000, p < .001. Which of the following is the most appropriate interpretation?

Accepted Answer

The correlation coefficient (r) of .11 indicates a positive, but small association between math scores and generalized anxiety. The large sample size (n=1,000) and low p-value (<.001) suggest that this association is statistically significant and likely to be present in the population. However, the correlation coefficient of .11 indicates only a weak association, which may have limited practical significance.

Question 18

You collected data from one group of students using a well-known state anxiety scale. You then administer a less well-known state depression scale. You are interested in how scores on these scales are associated. Which of the following tests is most appropriate?

Accepted Answer

A correlation test is appropriate for examining the relationship between scores on two different scales, in this case the state anxiety scale and the state depression scale. The other tests listed are not appropriate for this type of analysis.

Question 19

You have conducted a study with twelve people. Each person gave two blood samples, one before watching Friday the 13th part 14, and one after watching it. You measure cortisol levels. You subtract these scores (after level minus before level) to measure the effect of the movie on cortisol level. The mean difference is +4 micrograms per deciliter. The difference has a standard deviation of 10. You conduct a one-sample (or paired) t-test. What t value do you get (to two decimal places)?

Accepted Answer

The t value is calculated using the formula: $ t = \frac{\text{mean difference}}{\text{standard deviation of the difference} / \sqrt{n}} $, where n is the number of pairs. Plugging in the given values: $ t = \frac{4}{10 / \sqrt{12}} = 1.39 $.

Question 20

For the above example, what is the correct degrees of freedom to use to look up in a t-test?

Accepted Answer

To calculate degrees of freedom for a t-test, subtract 1 from the sample size, which in this case is 12-1=11. Therefore, the correct degrees of freedom to use would be 11. Option D is incorrect as using a z-table or an infinite number for a t-table is only appropriate when dealing with a normal distribution, which is not the case here.

Quiz 16: Inferential Statistics