Question 1

Which of the following statements about probability is TRUE?

Accepted Answer

The probability of an event must be between 0 and 1, inclusive.

Question 2

A researcher flips a coin 100 times and observes 55 heads. What is the empirical probability of getting heads in this experiment?

Accepted Answer

$$ \frac{55}{100} $$

Question 3

If the probability of an event A is 0.3, what is the probability that event A does NOT occur?

Accepted Answer

$$ 0.7 $$

Question 4

Which of the following best describes a standard normal distribution?

Accepted Answer

A normal distribution with mean 0 and standard deviation 1.

Question 5

A z-score of 2.0 means:

Accepted Answer

The value is 2 standard deviations above the mean.

Question 6

If a data value has a z-score of $$-1.5$$, what does this indicate?

Accepted Answer

The value is 1.5 standard deviations below the mean.

Question 7

Which formula is used to calculate the z-score for a value $$x in a $$normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$ z = \frac{x - \mu}{\sigma} $$

Question 8

A hospital administrator wants to estimate the proportion of patients who recover within 3 days. Which of the following best describes the margin of error for the sample proportion?

Accepted Answer

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

Question 9

Which of the following is NOT a requirement for the sample proportion $$\hat{p} to $$have an approximately normal distribution?

Accepted Answer

The population must be normally distributed.

Question 10

A 95% confidence interval for a population mean is calculated as $$ (50, 60) . $$Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 11

Which of the following is the correct null hypothesis for testing whether the average commute time in a city is 30 minutes?

Accepted Answer

$$ H_0$: \mu = 30 $$

Question 12

A researcher is testing $$ H_0$: p = 0.5 $$ against $$ H_a: p \u003e 0.5 . $$What type of test is this?

Accepted Answer

Right-tailed test

Question 13

Which of the following best describes the meaning of a p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.

Question 14

A sample of 100 batteries has a mean lifetime of 500 hours with a standard deviation of 50 hours. What is the z-score for a battery that lasts 600 hours?

Accepted Answer

$$ z = \frac{600 - 500}{50} = 2 $$

Question 15

Which of the following is a correct statement about confidence intervals?

Accepted Answer

Increasing the sample size decreases the margin of error.

Question 16

A pharmaceutical company wants to test if a new drug is more effective than the current standard. Which is the correct alternative hypothesis?

Accepted Answer

$$ H_a: \mu \u003e \mu_0$ $$

Question 17

If a hypothesis test results in a p-value less than the significance level $$\alpha$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 18

Which of the following is a real-world example of using the Central Limit Theorem?

Accepted Answer

Estimating the average cholesterol level in a population using the means of many random samples.

Question 19

A sample proportion $$\hat{p} is 0.4 $$from a sample of 200. What is the standard error of $$\hat{p}$$?

Accepted Answer

$$ \sqrt{\frac{0.4 	imes 0.6}{200}} $$

Statistics Exam 2 Study Guide: Probability, Normal Distributions, Sampling, Estimation, and Hypothesis Testing

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