Q: If the probability of a patient recovering from a certain disease after treatment is 0.8, what is the probability that exactly 3 out of 5 patients recover?

$$P(X=3) = \binom{5}{3} (0.8)^3$ (0.2)^2$ = 10 \times 0.512 \times 0.04 = 0.2048$$

Q: Which formula is used to calculate the expected frequency in a chi-square test for independence?

$$E = \frac{(\text{row total}) \times (\text{column total})}{\text{grand total}}$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A pharmaceutical company wants to test whether a new drug is effective. They randomly assign 100 patients to receive the drug and 100 to receive a placebo. What type of study is this?

Accepted Answer

Experimental study

Question 3

Which of the following is a categorical variable?

Accepted Answer

Type of blood group (A, B, AB, O)

Question 4

Suppose the mean score on a statistics exam is 70 with a standard deviation of 10. If a student scores 85, what is their z-score?

Accepted Answer

$$z = \frac{85 - 70}{10} = 1.5$$

Question 5

A researcher collects data on the number of hours students study per week and their final exam scores. Which statistical method is most appropriate to analyze the relationship between these two variables?

Accepted Answer

Correlation analysis

Question 6

If the probability of a patient recovering from a certain disease after treatment is 0.8, what is the probability that exactly 3 out of 5 patients recover?

Accepted Answer

$$P(X=3) = \binom{5}{3} (0.8)^3$ (0.2)^2$ = 10 	imes 0.512 	imes 0.04 = 0.2048$$

Question 7

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

Accepted Answer

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 8

A 95% confidence interval for the mean systolic blood pressure in a population is (120, 130). Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the true mean systolic blood pressure lies between 120 and 130.

Question 9

A hospital administrator wants to know if the proportion of patients who recover after a new treatment is different from 0.7. Which hypothesis test should be used?

Accepted Answer

One-proportion z-test

Question 10

Which of the following is an example of a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 11

A researcher wants to compare the mean cholesterol levels between two independent groups: those who exercise regularly and those who do not. Which test is most appropriate?

Accepted Answer

Two-sample t-test

Question 12

Which formula is used to calculate the expected frequency in a chi-square test for independence?

Accepted Answer

$$E = \frac{(	ext{row total}) 	imes (	ext{column total})}{	ext{grand total}}$$

Question 13

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam score. Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 14

If a data set is skewed to the right, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 15

A researcher collects paired data on blood pressure before and after a new medication in the same group of patients. Which test should be used to analyze the difference?

Accepted Answer

Paired t-test

Question 16

Which of the following is the correct formula for the standard error of the mean when sampling from a population with standard deviation $$\sigma$$ and sample size $$n$$?

Accepted Answer

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

Question 17

A city council wants to know if the distribution of car colors in their city matches the national distribution. Which test should they use?

Accepted Answer

Chi-square goodness of fit test

Question 18

Which of the following is NOT an assumption of linear regression?

Accepted Answer

The independent variable is normally distributed.

Question 19

A sample of 36 students has a mean test score of 80 and a standard deviation of 12. What is the 95% confidence interval for the mean? (Assume normality and use $$z = 1.96)$$

Accepted Answer

$$80 \pm 1.96 	imes \frac{12}{6}$$,
$$= 80 \pm 3.92$$,
$$(76.08, 83.92)$$

Question 20

Which of the following best describes the purpose of a scatter plot?

Accepted Answer

To visually display the relationship between two quantitative variables.

MATH 1160 – Introduction to Statistics: Course Syllabus and Study Guide

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