Question 1

Which of the following best describes the difference between qualitative and quantitative data?

Accepted Answer

Qualitative data describe attributes or categories, while quantitative data are numerical measurements.

Question 2

A researcher wants to estimate the average height of adult males in a city. Which sampling method would best reduce bias?

Accepted Answer

Random sampling from the city’s population registry.

Question 3

Which measure of center is most appropriate for a dataset with extreme outliers?

Accepted Answer

Median

Question 4

Given a dataset with mean $$\mu = 50$$ and standard deviation $$\sigma = 10$$, what is the z-score for a value $$x = 70$$?

Accepted Answer

$$z = \frac{70 - 50}{10} = 2$$

Question 5

If two events $$A$$ and $$B$$ are mutually exclusive, which of the following is true?

Accepted Answer

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

Question 6

A fair die is rolled twice. What is the probability of getting a 6 on both rolls?

Accepted Answer

$$\frac{1}{36}$$

Question 7

Which formula represents the expected value $$E[X] of a $$discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$p_i$$?

Accepted Answer

$$E[X] = \sum x_i p_i$$

Question 8

In a binomial experiment with $$n = 10$$ trials and probability of success $$p = 0.3$$, what is the probability of exactly 3 successes?

Accepted Answer

$$P(X=3) = \binom{10}{3} (0.3)^3$ (0.7)^7$

Question 9

Which property is characteristic of the normal distribution?

Accepted Answer

It is symmetric about the mean.

Question 10

A hospital records the weights of newborns, which are normally distributed with mean $$\mu = 3.5 kg $$and standard deviation $$\sigma = 0.5 kg. $$What proportion of newborns weigh less than 3.0 kg?

Accepted Answer

Approximately $$0.16$$

Question 11

According to the Central Limit Theorem, as sample size increases, the sampling distribution of the sample mean:

Accepted Answer

Becomes more normal, regardless of the population distribution.

Question 12

A confidence interval for the mean using the z-table is appropriate when:

Accepted Answer

The sample size is large and the population standard deviation is known.

Question 13

For a large sample, the confidence interval for a proportion $$p is $$given by:

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 14

In hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 15

A pharmaceutical company tests a new drug on a small sample. Which test should be used to compare the mean effect to a known value?

Accepted Answer

One-sample t-test

Question 16

When comparing two proportions, which formula is used for the standard error in the confidence interval?

Accepted Answer

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

Question 17

A matched pairs t-test is most appropriate when:

Accepted Answer

The same subjects are measured before and after a treatment.

Question 18

Which statistic measures the strength and direction of a linear relationship between two variables?

Accepted Answer

Pearson correlation coefficient $$r$$

Question 19

Given the regression equation $$y = 2x + 5$$, what is the predicted value of $$y$$ when $$x = 3$$?

Accepted Answer

$$y = 2 	imes 3 + 5 = 11$$

STAT-I 301 Spring 2026: Structured Study Guide and Course Overview

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