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Statistics

David Freedman, Robert Pisani, Roger Purves

Chapter 20

Chance Errors in Sampling - all with Video Answers

Educators

CM

Chapter Questions

04:08

Problem 1

Complete the following table for the coin-tossing game.

Bryan Luo
Bryan Luo
Numerade Educator
04:50

Problem 2

A die is rolled one thousand times. The percentage of aces (..) should be around $\longrightarrow$ , give or take $\longrightarrow$ or so.
(a) The first step in solving this problem is
(i) computing the SD of the box.
(ii) computing the average of the box.
(iii) setting up the box model. Choose one option and explain. (b) Now solve the problem.

CM
Caroline Morales
Numerade Educator
06:06

Problem 3

A group of $50,000$ tax forms has an average gross income of $\$ 37,000,$ with an $S D$ of $\$ 20,000 .$ Furthermore, 20$\%$ of the forms have a gross income over $\$ 50,000 .$ A group of 900 forms is chosen at random for audit. To estimate the chance that between 19$\%$ and 21$\%$ of the forms chosen for audit have gross incomes over $\$ 50,000,$ a box model is needed.
(a) Should the number of tuckets in the box be 900 or $50,000$ ?
(b) Each ticket in the box shows
(c) True or false: the SD of the box is $\$ 20,000 .$
(d) True or false: the number of draws is 900.
(e) Find the chance (approximately) that between 19$\%$ and 21$\%$ of the forms chosen for audit have gross incomes over $\$ 50,000 .$\
(f) With the information given, can you find the chance (approximately) that between 996 and 11$\%$ of the forms chosen for audit have gross incomes over $\$ 75,000$ ? Either find the chance, or explain why you need more information.

Bryan Luo
Bryan Luo
Numerade Educator
03:06

Problem 4

As in exercise 3 except it is desired to find the chance (approximately) that the total gross income of the audited forms is over $\$ 33,000,000 .$ Work parts (a) through (d); then find the chance or explain why you need more information.

Sherrie Fenner
Sherrie Fenner
Numerade Educator
00:39

Problem 5

(Hypothetical.) On the average, hotel guests who take elevators weigh about 150 pounds with an $S D$ of about 35 pounds. An engineer is designing a large elevator for a convention hotel, to lift 50 such people. If she designs it to lift 4 tons, the chance it will be overloaded by a random group of 50 people is about $\longrightarrow$ Explain briefly.

Brandon Fox
Brandon Fox
Numerade Educator
01:32

Problem 6

The Census Bureau is planning to take a sample amounting to 1$/ 10$ of 1$\%$ of the population in each state in order to estimate the percentage of the population in that state earning over $\$ 100,000$ a year. Other things being equal:
(i) The accuracy to be expected in California (population 35 million) is about the same as the accuracy to be expected in Nevada (population 2 million).
(ii) The accuracy to be expected in California is quite a bit higher than in Nevada.
(iii) The accuracy to be expected in California is quite a bit lower than in Nevada.

AG
Ankit Gupta
Numerade Educator
03:31

Problem 7

Five hundred draws are made at random from the box
True or false, and explain:
(a) The expected value for the percentage of $1^{\prime}$ 's among the draws is exactly 25$\% .$
(b) The expected value for the percentage of 1 's among the draws is around $25 \%,$ give or take 2$\%$ or so.
(c) The percentage of 1 's among the draws will be around $25 \%,$ give or
(d) The percentage of 1 's among the draws will be exactly 25$\%$
(e) The percentage of $1^{\prime}$ s in the box is exactly 25$\%$ .
(f) The percentage of $1^{\prime}$ s in the box is around $25 \%,$ give or take 2$\%$ or so.

Bryan Luo
Bryan Luo
Numerade Educator
01:42

Problem 8

In a certain town, there are $30,000$ registered voters, of whom $12,000$ are Democrats. A survey organization is about to take a simple random sample of $1,000$ registered voters. There is about a $50-50$ chance that the percentage of Democrats in the sample will be bigger than $\longrightarrow$ Fill in the blank, and explain.

Filip Kokotovic
Filip Kokotovic
Numerade Educator
02:48

Problem 9

Six hundred draws will be made at random with replacement from the box The number of 1 's among the draws will be around or take $\quad$ or $\mathrm{so.}$

Bryan Luo
Bryan Luo
Numerade Educator
01:17

Problem 10

A coin is tossed $2,000$ times. Someone to compute the SE for the number of heads among the tosses as $\sqrt{2,000} \times 0.5 \approx 22 .$ Is this the right SE? Answer yes or no, and explain briefly.

Amany Waheeb
Amany Waheeb
Numerade Educator
02:47

Problem 11

A university has $25,000$ students, of whom $17,000$ are undergraduates. The housing office takes a simple random sample of 500 students; 357 out of the 500 are undergraduates. Fill in the blanks.
(a) For the number of undergraduates in the sample, the observed value is $\frac{\text { but the expected value is }}{\text { is }}$ but the expected value is
(b) For the percentage of undergraduates in the sample, the observed value

Bryan Luo
Bryan Luo
Numerade Educator
01:32

Problem 12

There are $50,000$ households in a certain city. The average number of persons age 16 and over living in each household is known to be $2.38 ;$ the $S D$ is 1.87 . A survey organization plans to take a simple random sample of 400 households, and interview all persons age 16 and over living in the sample households. The total number of interviews will be around $\longrightarrow$ give or take or so. Explain briefly.

Bryan Meares
Bryan Meares
Numerade Educator