Question 1

Which of the following best describes the primary purpose of using statistics in research?

Accepted Answer

To collect and interpret data in order to make informed decisions and draw conclusions

Question 2

A pharmaceutical company wants to test if a new drug is effective. Which statistical method should they use to compare the mean recovery times between a treatment group and a control group?

Accepted Answer

Two-sample t-test for independent means

Question 3

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 4

A histogram is most useful for which of the following tasks?

Accepted Answer

Displaying the frequency distribution of a continuous variable

Question 5

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

It states that the sampling distribution of the sample mean approaches normality as sample size increases

Question 6

Suppose a fair coin is flipped 10 times. What is the probability of getting exactly 5 heads? Use the binomial probability formula.

Accepted Answer

$$P(X=5) = \binom{10}{5} (0.5)^5$ (0.5)^5$

Question 7

Which of the following is NOT a measure of central tendency?

Accepted Answer

Variance

Question 8

A researcher wants to test if the proportion of left-handed students in a university differs from the national average of 10%. Which hypothesis test should be used?

Accepted Answer

One-sample z-test for proportions

Question 9

Which formula correctly calculates the sample variance $$s^2$$ for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^{n} (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 10

A hospital administrator wants to know if there is a relationship between smoking status (smoker/non-smoker) and the presence of lung disease (yes/no). Which statistical test is most appropriate?

Accepted Answer

Chi-square test for independence

Question 11

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we take many samples, about 95% of the confidence intervals calculated will contain the true population mean

Question 12

Which of the following is the formula for the standard error of the mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$SE = \frac{\sigma}{\sqrt{n}}$$

Question 13

A researcher collects data on the number of hours students study and their exam scores. Which statistical method should be used to determine if there is a linear relationship between the two variables?

Accepted Answer

Simple linear regression

Question 14

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars passing through an intersection in an hour

Question 15

If the probability of rain on any given day is 0.2, what is the probability that it will NOT rain tomorrow?

Accepted Answer

$$P(	ext{no rain}) = 1 - 0.2 = 0.8$$

Question 16

Which of the following is the correct formula for the z-score of a value $$x in a $$population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 17

A study finds a correlation coefficient $$r = 0.85$$ between two variables. Which of the following best describes the relationship?

Accepted Answer

A strong positive linear relationship

Question 18

Which of the following is a key assumption for using the normal approximation to the binomial distribution?

Accepted Answer

Both $$np \geq 5$$ and $$n(1-p) \geq 5$$

Question 19

Which of the following best describes the purpose of hypothesis testing in statistics?

Accepted Answer

To determine if there is enough evidence to support a specific claim about a population

Elementary Statistical Methods – Course Syllabus and Study Guide

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