Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable that can only take specific, countable values, such as the number of students in a class.

Question 2

A pharmaceutical company wants to estimate the proportion of patients who experience side effects from a new drug. Which formula should they use to construct a confidence interval for the population proportion?

Accepted Answer

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

Question 3

Which graphical representation is most appropriate for displaying the distribution of a categorical variable, such as favorite ice cream flavor?

Accepted Answer

Bar plot

Question 4

A researcher collects data on the heights of 100 students. Which measure of central tendency is most appropriate if the data contains several extreme outliers?

Accepted Answer

Median

Question 5

A hospital administrator wants to know the probability that at least one out of five randomly selected patients will test positive for a rare disease, given the probability of a positive test is 0.02. Which probability distribution should be used?

Accepted Answer

Binomial distribution

Question 6

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

Accepted Answer

It states that the distribution of sample means approaches a normal distribution as sample size increases, regardless of the population's distribution.

Question 7

A quality control manager wants to test if the mean weight of cereal boxes is different from the advertised weight of 500g. The population standard deviation is unknown and the sample size is 15. Which test should be used?

Accepted Answer

T-test for population mean

Question 8

Which formula is used to calculate the margin of error for a confidence interval estimating a population mean when the population standard deviation is unknown?

Accepted Answer

$$ t \cdot \frac{s}{\sqrt{n}} $$

Question 9

A school principal wants to determine if the proportion of students passing a math test this year is higher than last year. Which hypothesis test should be used?

Accepted Answer

Z-test for population proportion

Question 10

Which of the following is NOT a property of a normal distribution?

Accepted Answer

It has a skewed tail to the right.

Question 11

A researcher wants to estimate the variance of blood pressure readings in a population. Which distribution should be used to construct a confidence interval for the variance?

Accepted Answer

Chi-square distribution

Question 12

Which formula is used to calculate the binomial probability of exactly $$k$$ successes in $$n$$ trials, with probability $$p of $$success?

Accepted Answer

$$ P(X = k) = \frac{n!}{k!(n-k)!} p^k (1-p$$)^{n-k}$$ $$

Question 13

A scientist wants to test the claim that the variance of a chemical's concentration in water samples is less than 0.5. Which hypothesis test should be used?

Accepted Answer

Chi-square test for variance

Question 14

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

Accepted Answer

Rejecting a true null hypothesis.

Question 15

A city planner wants to know if the average commute time has changed from last year. The sample mean is 35 minutes, sample standard deviation is 8 minutes, and sample size is 50. Which formula should be used to calculate the test statistic for a hypothesis test about the mean?

Accepted Answer

$$ t = \frac{ \bar{x} - \mu }{ \frac{s}{\sqrt{n}} } $$

Question 16

Which of the following is a real-world example of using the addition rule of probability?

Accepted Answer

Calculating the probability that a randomly selected person is either a smoker or has high blood pressure.

Question 17

A biologist wants to determine the sample size needed to estimate the mean weight of frogs within 2 grams of the true mean, with 95% confidence and a population standard deviation of 5 grams. Which formula should be used?

Accepted Answer

$$ n = \left( \frac{ z \cdot \sigma }{ E } \$$right)^2$$ $$

Question 18

Which of the following is NOT a requirement for using the binomial probability formula?

Accepted Answer

There must be more than two possible outcomes for each trial.

Question 19

A sociologist wants to test if the mean income in a city is greater than $$50,000. The null hypothesis is $$ $$H_0$$: \mu = 50,000 $$ and the alternative hypothesis is $$ $$H_1$$: \mu \u003e 50,000 $. Which type of test is this?

Accepted Answer

Right-tailed test

Introductory Statistics (MAT143) – Course Syllabus and Topic Overview

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