Q: In a Gallup Poll of 1005 individuals, 452 thought they were worse off financially than a year ago. Find the margin of error for a 95% confidence interval for the proportion. (Round to four decimal places.)

$$E = 1.96 \times \sqrt{\dfrac{0.4498 \times 0.5502}{1005}} = 0.0307$$

Q: Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hour. For a 95% confidence level, what is the margin of error? (Round to two decimal places.)

$$E = t_{0.025,9} \times \dfrac{0.78}{\sqrt{10}} = 0.51$$

Question 1

A market researcher selects 500 people from each of 10 cities to participate in a survey. Which type of sampling is being used?

Accepted Answer

Stratified sampling

Question 2

Which of the following is measured at the interval level of measurement?

Accepted Answer

Body temperatures of newborn babies in a hospital

Question 3

A researcher wants to determine if screen brightness affects battery life. She randomly selects 30 laptops, increases the brightness on 15, and leaves the other 15 at normal brightness, then measures battery life. What type of study is this?

Accepted Answer

Experiment

Question 4

A statistical analyst obtains data about ankle injuries by examining a hospital's records from the past 3 years. What type of observational study is this?

Accepted Answer

Retrospective study

Question 5

The number of freshmen entering college in a certain year is 621. Is this value from a discrete or continuous data set?

Accepted Answer

Discrete

Question 6

A random sample of 100 subscribers is taken and their mean income is found to be $27,500. Is this value a parameter or a statistic?

Accepted Answer

Statistic

Question 7

Select a student in your college: The student is a freshman and a sophomore. Are these events mutually exclusive?

Accepted Answer

Yes, they are mutually exclusive

Question 8

A card is drawn from a deck of cards without replacement. Then another card is drawn. Are these events independent or dependent?

Accepted Answer

Dependent

Question 9

An inspector must select 3 tests to perform in a certain order on a manufactured part. He has a choice of 7 tests. How many ways can he perform 3 different tests?

Accepted Answer

$$7 	imes 6 	imes 5 = 210$$

Question 10

At a used-book sale, there are 70 adult nonfiction, 30 adult fiction, 60 children’s nonfiction, and 100 children’s fiction books. If a book is selected at random, what is the probability that it is a children’s book?

Accepted Answer

$$\dfrac{160}{260} = 0.615$$

Question 11

If the probability that it will rain tomorrow is 0.20, what is the probability that it will not rain tomorrow?

Accepted Answer

$$1 - 0.20 = 0.80$$

Question 12

A survey of 125 students found that 50 have Facebook, 102 have Instagram, and 37 have both. What is the probability that a randomly selected student has Facebook or Instagram? (Write as a fraction and decimal rounded to 2 decimal places.)

Accepted Answer

$$\dfrac{115}{125} = 0.92$$

Question 13

47.5% of children say they prefer chocolate ice cream. If 4 children are randomly selected, what is the probability that at least one prefers chocolate ice cream? (Use the binomial probability formula.)

Accepted Answer

$$1 - (0.525)^4$ = 0.924$$

Question 14

A certain medical procedure has an 85% chance of success. The surgery is performed on 8 patients. What is the probability that at least 5 surgeries are successful? (Use the binomial probability formula.)

Accepted Answer

$$\sum_{k=5}^{8} \binom{8}{k} (0.85)^k (0.15$$)^{8-k}$$

Question 15

Find the area under the standard normal curve to the left of $$z = 1.31 (i.e$$., $$P(z \u003c 1.31)).$$

Accepted Answer

$$0.9049$$

Question 16

Find the critical value needed to construct an 85% confidence interval for a population proportion.

Accepted Answer

$$z_{\alpha/2} = 1.44$$

Question 17

The national average SAT score is 1019 with $$\sigma = 100. $$What SAT score is at the 85th percentile?

Accepted Answer

$$x = 1019 + (1.04)(100) = 1123$$

Question 18

In a Gallup Poll of 1005 individuals, 452 thought they were worse off financially than a year ago. Find the margin of error for a 95% confidence interval for the proportion. (Round to four decimal places.)

Accepted Answer

$$E = 1.96 	imes \sqrt{\dfrac{0.4498 	imes 0.5502}{1005}} = 0.0307$$

Question 19

Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hour. For a 95% confidence level, what is the margin of error? (Round to two decimal places.)

Accepted Answer

$$E = t_{0.025,9} 	imes \dfrac{0.78}{\sqrt{10}} = 0.51$$

Question 20

Given the following paired data for shoe size and height: (8.5, 67), (9.5, 70), (11, 73.5), (12, 75), (13, 78), (8, 66). What is the linear correlation coefficient $$r$$? (Round to two decimal places.)

Accepted Answer

$$r = 0.99$$

Comprehensive Step-by-Step Guidance for Statistics Final Exam Practice

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