Question 1

Which of the following is NOT a level of measurement commonly used for classifying data sets?

Accepted Answer

Critical

Question 2

Given the data set: $$2.1, 4.0, 5.9, 6.8, 6.9, 7.2, 8.0, 8.2, 8.7$$, what is the median?

Accepted Answer

$$6.9$$

Question 3

A hospital records the number of patients arriving at the emergency room per hour. Which probability distribution is most appropriate for modeling this scenario?

Accepted Answer

Poisson distribution

Question 4

A fair coin is tossed 10 times. What is the probability of getting exactly 6 heads? Use the binomial formula: $$P(X = k) = \frac{n!}{k!(n-k)!} p^k (1-p$$)^{n-k}$$, where n=10$, k=6$, p=0.5$.

Accepted Answer

$$0.205$$

Question 5

A researcher wants to estimate the mean cholesterol level in a population. The sample mean is $$200 mg/dL$$, the standard deviation is $$20 mg/dL$$, and the sample size is $$100. $$What is the $$95\%$$ confidence interval for the mean? (Use $$z=1.96$$ for $$95\%$$ confidence.)

Accepted Answer

$$[198.04, 201.96]$$

Question 6

Which of the following statements about the standard deviation is TRUE?

Accepted Answer

It measures the spread of data around the mean.

Question 7

A study finds that $$60\% of $$adults prefer tea over coffee. If 5 adults are randomly selected, what is the probability that exactly 3 prefer tea? (Use the binomial formula with $$n=5$$, $$k=3$$, $$p=0.6.)$$

Accepted Answer

$$0.3456$$

Question 8

Which of the following is a correct interpretation of a $$p-$$value in hypothesis testing?

Accepted Answer

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

Question 9

A sample of 100 batteries has a mean lifetime of $$500$$ hours and a standard deviation of $$50$$ hours. What is the standard error of the mean?

Accepted Answer

$$5$$

Question 10

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, which of the following best describes the relationship?

Accepted Answer

Strong negative linear relationship

Question 11

A Poisson process models the number of cars passing through a toll booth at a rate of $$\lambda = 3$$ cars per minute. What is the probability that exactly 5 cars pass through in a given minute? (Use $$P(X=k) = \frac{e$$^{-\lambda}$$ \lambda^k}{k!})$$

Accepted Answer

$$0.1008$$

Question 12

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

Accepted Answer

The sample means are equal.

Question 13

A regression analysis yields the equation $$\hat{y} = 2 + 0.5x. $$What is the predicted value of $$y$$ when $$x = 8$$?

Accepted Answer

$$6$$

Question 14

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

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 15

A pharmaceutical company tests a new drug and finds a $$p-$$value of $$0.03$$ when testing at a $$0.05$$ significance level. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; the result is statistically significant.

Question 16

Which of the following is a discrete random variable?

Accepted Answer

The number of cars in a parking lot

Question 17

A data set has a mean of $$10$$ and a standard deviation of $$2. $$What is the $$z-$$score for a value of $$14$$?

Accepted Answer

$$2$$

Question 18

Which of the following is the formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 19

A survey of 200 people finds that 120 prefer product A and 80 prefer product B. What is the sample proportion of people who prefer product A?

Accepted Answer

$$0.60$$

Question 20

Which of the following is a correct interpretation of the coefficient of determination $$R^2 in $$regression analysis?

Accepted Answer

The proportion of the variance in the dependent variable that is predictable from the independent variable.

Comprehensive Study Notes: Statistics Final Exam Review

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