Question 1

Which of the following best describes a nominal measurement scale?

Accepted Answer

It categorizes data without any order or ranking.

Question 2

A researcher wants to visualize the relationship between two categorical variables, such as gender and preferred beverage. Which method is most appropriate?

Accepted Answer

A clustered bar chart

Question 3

Given a dataset with a mean of 50 and a standard deviation of 10, what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

Approximately 95%

Question 4

Chebyshev’s theorem states that for any dataset, at least what percentage of values lie within $$k$$ standard deviations of the mean, where $$k \u003e 1$$?

Accepted Answer

$$1 - \frac{1}{k^2$}$$

Question 5

A contingency table is used to:

Accepted Answer

Display the frequency distribution of two categorical variables

Question 6

If the probability of event A is 0.3 and the probability of event B is 0.5, and A and B are mutually exclusive, what is the probability of A or B occurring?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) = 0.8$$

Question 7

A binomial experiment consists of 10 trials with a probability of success $$p = 0.4. $$What is the probability of exactly 3 successes?

Accepted Answer

$$P(X=3) = \binom{10}{3} (0.4)^3$ (0.6)^7$

Question 8

In a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the $$z-$$score for $$X = 130$$?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2$$

Question 9

A random sample of 50 students is taken from a university population. Which sampling method is being used if every student has an equal chance of being selected?

Accepted Answer

Simple random sampling

Question 10

A confidence interval for the mean is calculated as $$\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}. $$Which condition must be met for this formula to be valid?

Accepted Answer

The population standard deviation $$\sigma$$ must be known.

Question 11

A pharmaceutical company wants to estimate the proportion of patients who experience side effects from a new drug. Which formula should they use to determine the minimum sample size required for a desired margin of error $$E$$?

Accepted Answer

$$n = \frac{z_{\alpha/2}^2 p(1-p)}{E^2$}$$

Question 12

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis

Question 13

A hospital claims that the average wait time in its emergency room is less than 30 minutes. Which is the correct null hypothesis for a one-sample $$z-$$test?

Accepted Answer

$$H_0$$: \mu = 30$$

Question 14

In a matched-pairs sampling scenario, which formula is used to construct a confidence interval for the mean difference?

Accepted Answer

$$\bar{d} \pm t_{\alpha/2} \frac{s_d}{\sqrt{n}}$$

Question 15

In multiple linear regression, what does the adjusted $$R^2$$ statistic account for that the regular $$R^2$$ does not?

Accepted Answer

The number of predictors in the model

Question 16

Which formula is used to test the significance of an individual regression coefficient $$\beta_j$$?

Accepted Answer

$$t = \frac{\hat{\beta}_j}{SE(\hat{\beta}_j)}$$

Question 17

A researcher wants to test whether two population proportions are equal. Which test statistic should be used?

Accepted Answer

$$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1$} + \frac{1}{n_2$}\right)}}$$

Question 18

Which of the following is a dummy variable in regression analysis?

Accepted Answer

A variable coded as 0 or 1 to represent categories

Question 19

In hypothesis testing, the critical value approach involves:

Accepted Answer

Comparing the test statistic to a threshold to decide whether to reject the null hypothesis

Question 20

A general test of linear restrictions in regression analysis is conducted using which statistic?

Accepted Answer

$$F = \frac{(SSR_{restricted} - SSR_{unrestricted})/q}{SSR_{unrestricted}/(n-k-1)}$$

Introductory Statistics: Exam Preparation Study Guide

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