Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use data from a sample to make generalizations about a population.

Question 2

A researcher wants to study the effect of a new medication on blood pressure. She randomly assigns 100 patients to receive the medication and 100 to receive a placebo. Which type of experimental design is this?

Accepted Answer

Randomized controlled experiment

Question 3

Which of the following variables is best classified as discrete?

Accepted Answer

The number of students in a classroom

Question 4

A data set has a mean of 50 and a standard deviation of 5. According to the Empirical Rule, approximately what percentage of the data falls between 40 and 60?

Accepted Answer

Approximately 68%

Question 5

Which of the following is the correct formula for the variance $$s^2 of a $$sample of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 6

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 7

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

Accepted Answer

The CLT states that 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 hospital administrator wants to estimate the average length of stay for patients. She takes a random sample of 64 patients and finds a mean stay of 5 days with a standard deviation of 2 days. Construct a 95% confidence interval for the mean length of stay. (Use $$z^* = 1.96)$$

Accepted Answer

$$5 \pm 0.49$$

Question 9

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

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 10

A researcher is testing whether a new teaching method improves test scores. The null hypothesis is $$H_0$$: \mu = 75$$ and the alternative is H_1$: \mu \u003e 75. $$The sample mean is 78, the sample standard deviation is 10, and the sample size is 25. What is the value of the test statistic?

Accepted Answer

$$z = 1.5$$

Question 11

Which of the following best describes the difference between independent and dependent samples?

Accepted Answer

Independent samples are selected so that the selection of one sample does not influence the selection of the other, while dependent samples are paired or matched in some way.

Question 12

A study compares the mean cholesterol levels of two groups: one on a new diet and one on a standard diet. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 13

Which of the following is the correct formula for the binomial probability of getting exactly $$k$$ successes in $$n$$ independent trials with probability $$p of $$success?

Accepted Answer

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

Question 14

A researcher wants to test if there is an association between smoking status (smoker/non-smoker) and lung disease (present/absent) in a population. Which statistical test should be used?

Accepted Answer

Chi-square test of independence

Question 15

Which of the following is NOT an assumption of the one-way ANOVA?

Accepted Answer

The samples are dependent.

Question 16

Given the regression equation $$\hat{y} = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 14$$

Question 17

A sample of 100 students is surveyed, and 40 report using public transportation. What is the 95% confidence interval for the proportion of students who use public transportation? (Use $$z^* = 1.96)$$

Accepted Answer

$$0.4 \pm 0.098$$

Question 18

Which of the following best describes the relationship between correlation and causation?

Accepted Answer

Correlation does not imply causation.

Question 19

A box-and-whisker plot is most useful for displaying which of the following?

Accepted Answer

The five-number summary of a data set

Question 20

Which of the following is the correct formula for the standard error of the mean for a sample of size $$n$$ with standard deviation $$s$$?

Accepted Answer

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

STAT C1000: Introduction to Statistics – Course Syllabus and Topical Outline Study Guide

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