Q: A company records the number of defective products in 20 batches as follows: 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10. What is the five-number summary for this data set?

$$\text{Min} = 1,\ Q_1$ = 3,\ \text{Median} = 5,\ Q_3$ = 7,\ \text{Max} = 10$$

Q: A sample of 15 light bulbs has a sample variance of $$s^2 = 4$. What is the 90% confidence interval for the population variance $$\$$sigma^2$$? (Use $$\$$chi^2$$_{0.05,14} = 23.685$$, $$\$$chi^2$$_{0.95,14} = 6.571)$$

$$\left( \dfrac{14 \times 4}{23.685},\ \dfrac{14 \times 4}{6.571} \right)$$

Question 1

A hospital administrator wants to summarize the number of patients admitted each day over a month. Which of the following graphical methods is most appropriate for displaying the frequency of daily admissions?

Accepted Answer

Histogram

Question 2

Given the following data set representing the number of books read by 10 students in a semester: 2, 3, 3, 4, 5, 5, 5, 6, 7, 8. What is the mode of this data set?

Accepted Answer

$$5$$

Question 3

A company records the number of defective products in 20 batches as follows: 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10. What is the five-number summary for this data set?

Accepted Answer

$$	ext{Min} = 1,\ Q_1$ = 3,\ 	ext{Median} = 5,\ Q_3$ = 7,\ 	ext{Max} = 10$$

Question 4

A fair six-sided die is rolled twice. What is the probability that both rolls result in an even number?

Accepted Answer

$$\dfrac{1}{4}$$

Question 5

A bag contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are blue?

Accepted Answer

$$\dfrac{1}{15}$$

Question 6

Which of the following formulas correctly calculates the variance $$\$$sigma^2$$ of a population with N$ values x_1$, x_2$, ..., x_N$$ and mean $$\mu$$?

Accepted Answer

$$\$$sigma^2$$ = \dfrac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2$

Question 7

A discrete random variable $$X$$ has the following probability distribution: $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is the expected value $$E[X]$$?

Accepted Answer

$$1.1$$

Question 8

A multiple-choice test has 5 questions, each with 4 possible answers (only one correct). If a student guesses on all questions, what is the probability that they get exactly 2 questions correct?

Accepted Answer

$$\binom{5}{2} \left(\dfrac{1}{4}\$$right)^2$$ \left(\dfrac{3}{4}\$$right)^3$$

Question 9

Suppose the heights of adult men in a city are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What is the $$z-$$score for a man who is 76 inches tall?

Accepted Answer

$$2$$

Question 10

A sample of 25 students has a mean test score of 80 and a standard deviation of 10. Construct a 95% confidence interval for the population mean, assuming the scores are normally distributed. (Use $$t_{0.025,24} \approx 2.064)$$

Accepted Answer

$$80 \pm 4.13$$

Question 11

A researcher wants to test if a new medication changes the average recovery time from a certain illness. The null hypothesis is $$H_0$$: \mu = 10$$ days. The alternative hypothesis is H_1$: \mu 
eq 10$$ days. What type of test is this?

Accepted Answer

Two-tailed test

Question 12

Which of the following is the correct formula for the $$z-$$score of a value $$x in a $$population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 13

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. Which of the following best describes this relationship?

Accepted Answer

Strong positive linear correlation

Question 14

If the regression equation for predicting weight ($$y) $$from height ($$x) is$$ $$y = 2x + 10$$, what is the predicted weight for a person who is 65 inches tall?

Accepted Answer

$$140$$

Question 15

A quality control manager wants to estimate the proportion of defective items in a large shipment. Out of a random sample of 200 items, 16 are defective. Construct a 95% confidence interval for the proportion of defective items. (Use $$z_{0.025} = 1.96)$$

Accepted Answer

$$0.08 \pm 0.037$$

Question 16

Which of the following situations is best modeled by a binomial distribution?

Accepted Answer

Counting the number of heads in 10 flips of a fair coin

Question 17

A sample of 15 light bulbs has a sample variance of $$s^2 = 4$. What is the 90% confidence interval for the population variance $$\$$sigma^2$$? (Use $$\$$chi^2$$_{0.05,14} = 23.685$$, $$\$$chi^2$$_{0.95,14} = 6.571)$$

Accepted Answer

$$\left( \dfrac{14 	imes 4}{23.685},\ \dfrac{14 	imes 4}{6.571} ight)$$

Question 18

A researcher wants to test if the variance of weights of apples in an orchard is greater than $$1.5^2$$ ounces$$^2. $$What is the appropriate null hypothesis $$H_0$$?

Accepted Answer

$$H_0$$: \$$sigma^2$$ \leq 2.25$$

Question 19

A factory produces light bulbs with a mean lifetime of 1200 hours and a standard deviation of 100 hours. If a random sample of 36 bulbs is selected, what is the standard deviation of the sample mean?

Accepted Answer

$$\dfrac{100}{6}$$

Statistics Course Syllabus: Key Topics and Learning Objectives

Guida di studio - Domande di pratica

Study guide - Flashcard