Question 1

A hospital administrator wants to estimate the proportion of patients who recover within 3 days after a new treatment. She takes a random sample of 100 patients and finds that 60 recovered within 3 days. What is the point estimate for the population proportion of patients who recover within 3 days?

Accepted Answer

$$0.60$$

Question 2

Which of the following statements about probability is TRUE?

Accepted Answer

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

Question 3

A researcher is comparing the frequency of a rare genetic mutation in two populations. Which type of probability is she using when she calculates the proportion of individuals with the mutation in her sample?

Accepted Answer

Empirical probability

Question 4

If the probability that a randomly selected student passes a statistics exam is $$0.8$$, what is the probability that the student does NOT pass the exam?

Accepted Answer

$$0.2$$

Question 5

A standard normal distribution has a mean ($$\mu) $$and standard deviation ($$\sigma) of$$:

Accepted Answer

$$\mu = 0$$, $$\sigma = 1$$

Question 6

A z-score of $$-2 in a $$standard normal distribution indicates that the data value is:

Accepted Answer

2 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 sample of 50 batteries has a mean lifetime of 100 hours and a standard deviation of 10 hours. What is the standard error of the mean?

Accepted Answer

$$\frac{10}{\sqrt{50}}$$

Question 9

Which of the following best describes the Central Limit Theorem?

Accepted Answer

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

Question 10

A pharmaceutical company wants to estimate the mean recovery time for a new drug. They collect a sample and calculate a 95% confidence interval for the mean. What does the 95% confidence level mean?

Accepted Answer

If the study were repeated many times, about 95% of the calculated intervals would contain the true population mean.

Question 11

Which of the following is NOT a requirement for using the normal approximation for the sampling distribution of the sample proportion?

Accepted Answer

The sample mean is greater than the sample size.

Question 12

A researcher tests whether a new teaching method improves test scores. The null hypothesis is $$H_0$$: \mu = 75$$ and the alternative hypothesis is H_a$$: \mu \u003e 75$$. What type of test is this?

Accepted Answer

Right-tailed test

Question 13

Which of the following statements about hypothesis testing is correct?

Accepted Answer

The null hypothesis ($$H_0) $$states that there is no effect or no difference.

Question 14

A sample proportion is calculated as $$\hat{p} = \frac{x}{n}. If$$ $$x = 30$$ and $$n = 200$$, what is $$\hat{p}$$?

Accepted Answer

$$0.15$$

Question 15

Which of the following would increase the margin of error in a confidence interval for a population mean?

Accepted Answer

Increasing the standard deviation

Question 16

A student calculates a z-score of $$1.5$$ for her exam score. What does this mean?

Accepted Answer

Her score is 1.5 standard deviations above the mean.

Question 17

Which of the following is the correct formula for the margin of error ($$E) $$for estimating a population proportion at a given confidence level?

Accepted Answer

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

Question 18

A two-tailed hypothesis test is appropriate when:

Accepted Answer

The alternative hypothesis states that the parameter is not equal to a value.

Question 19

A scientist wants to know if the average weight of a species of fish in a lake is different from 5 kg. Which is the correct way to write the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 5$$, H_a$$: \mu 
eq 5$$

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

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