Question 1

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

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 2

A researcher flips a fair coin 6 times. What is the probability of getting exactly 2 heads? Use the binomial formula $$f(X = k; n, p) = \frac{n!}{k!(n-k)!} p^k (1-p$$)^{n-k}$$ with n=6$, k=2$, p=0.5$.

Accepted Answer

$$0.234$$

Question 3

Which of the following distributions is best represented by a histogram where all possible values have equal frequency?

Accepted Answer

Uniform distribution

Question 4

Given a normal distribution with mean $$\mu = 1150$$ and standard deviation $$\sigma = 150$$, what is the $$z-$$score for a value $$x = 1380$$? Use the formula $$z = \frac{x - \mu}{\sigma}.$$

Accepted Answer

$$1.53$$

Question 5

A p-value is used in hypothesis testing to:

Accepted Answer

Describe how likely the observed data would be if the null hypothesis were true.

Question 6

Which of the following is NOT a requirement for the Central Limit Theorem to apply?

Accepted Answer

The population must be normally distributed.

Question 7

A forester samples 150 trees and finds 65 host a specific epiphyte. She tests $$H_0$$: p \leq 0.4$$ vs H_1$: p \u003e 0.4. $$Using the normal approximation, what is the test statistic? Use $$T = \frac{X - np}{\sqrt{np(1-p)}}$$ with $$X=65$$, $$n=150$$, $$p=0.4.$$

Accepted Answer

$$0.833$$

Question 8

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

It is always skewed to the right.

Question 9

If the probability mass function (PMF) for rolling a fair six-sided die is $$f(x) = P(X = x)$$, what is $$f(5)$$?

Accepted Answer

$$\frac{1}{6}$$

Question 10

A marketing team surveys 1,000 people and finds 630 remember an ad. Test $$H_0$$: p \leq 0.6$$ vs H_1$: p \u003e 0.6. $$What is the test statistic? Use $$T = \frac{X - np}{\sqrt{np(1-p)}}$$ with $$X=630$$, $$n=1000$$, $$p=0.6.$$

Accepted Answer

$$1.94$$

Question 11

Which of the following best describes a probability density function (PDF)?

Accepted Answer

A function that gives the probability that a continuous random variable falls within a particular range of values.

Question 12

Which of the following is the correct formula for the cumulative distribution function (CDF) for a fair six-sided die?

Accepted Answer

$$F(X) = P(X \leq x) = \frac{x}{6}$$, $$x = 1, ..., 6$$

Question 13

A university surveys 1,200 students and finds 930 support a new platform. Test $$H_0$$: p \leq 0.75$$ vs H_1$: p \u003e 0.75. $$What is the sample proportion?

Accepted Answer

$$0.775$$

Question 14

Which of the following is a property of the standard normal distribution?

Accepted Answer

Mean $$= 0$$, standard deviation $$= 1$$

Question 15

Which test would you use to determine if two categorical variables are related?

Accepted Answer

Chi-square test of independence

Question 16

If a test statistic falls in the critical region, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 17

Which of the following is the correct formula for the binomial probability mass function?

Accepted Answer

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

Question 18

Which of the following is a real-world example of a Bernoulli trial?

Accepted Answer

Tossing a coin once

Week 3 Study Guide: Inference for Counts and Proportions, Probability Distributions, and Hypothesis Testing

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