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Chapter 8: Q.6 (page 477)

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal.

Identify the following:

a. x炉 = _____

b. 蟽 = _____

c. n = _____

Short Answer

Expert verified

The value of

a). x炉=8.2

b).蟽=2.2

c).n=200

Step by step solution

01

Part (a) Step 1: Given Information 

The sample mean is 8.2 minutes.
02

Part (a) Step 2: Explanation 

The sample mean is the average (or mean) value of a group of numbers drawn from a larger population of numbers, where "population" refers to all relevant data, whether or not it has been gathered.
The sample mean is 8.2minutes.
03

Part (b) Step 1: Given Information 

There is a known standard deviation of 2.2 minutes.

04

Part (b) Step 2: Explanation 

The standard deviation is a measurement of a set of values' variation or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are dispersed across a larger range.

There is a known standard deviation of 2.2minutes.

05

Part (c) Step 1: Given Information 

The Bureau surveys 200 people.

06

Part (c) Step 2: Explanation 

The number of individual samples utilized in an experiment is referred to as the sample size.

The Bureau surveys 200people.

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Most popular questions from this chapter

Using the same mean, standard deviation, and level of confidence, suppose that n were 69 instead of 25. Would the error bound become larger or smaller? How do you know?

If the Census did another survey, kept the error bound the same, and surveyed only 50 people instead of 200, what would happen to the level of confidence? Why?

Define the random variable X炉{"x":[[4,22,36],[6,35],[5.647456684472792,6.517307794504744,6.517307794504744,8.257010014568648,9.1268611246006,9.996712234632552,12.606265564728409,13.476116674760362,14.345967784792315,16.08567000485622,16.95552111488817,17.825372224920123,18.695223334952075,20.43492555501598,21.30477666504793,22.174627775079884,23.044478885111836,23.914329995143788,24.78418110517574,25.654032215207693,26.523883325239645,27.393734435271597,27.393734435271597,28.26358554530355,29.1334366553355,29.1334366553355,30.003287765367453,30.873138875399405,31.742989985431358,32.61284109546331]],"y":[[9,59,116],[115,9],[-7.088088802556169,-7.088088802556169,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-8.827791022620074,-8.827791022620074,-8.827791022620074,-9.697642132652026,-9.697642132652026,-9.697642132652026,-9.697642132652026,-9.697642132652026]],"t":[[0,0,0],[0,0],[1648475418436,1648475418678,1648475418692,1648475418709,1648475418727,1648475418743,1648475418760,1648475418776,1648475418791,1648475418810,1648475418826,1648475418842,1648475418859,1648475418875,1648475418892,1648475418910,1648475418925,1648475418942,1648475418965,1648475419009,1648475419026,1648475419076,1648475419105,1648475419118,1648475419134,1648475419146,1648475419161,1648475419180,1648475419242,1648475419292]],"version":"2.0.0"}in words.

122. Stanford University conducted a study of whether running is healthy for men and warner overage 50. During the first eight years of the study, 1.5%of the 451members of the 50-Plus Fatness Association died. We are interested in the proportion of people over 50who ran and tied in the same eight-year period.

a. Define the random variablesXandFin words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 97%confidence interval for the population proportion of people average50 we ran and died in the same eight-year period.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a " 97%confidence interval" means for this study.

A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 600students and finds that 480are against the new legislation.

a. Compute a 90% confidence interval for the true percent of students who are against the new legislation, and interpret the confidence interval.

b.In a sample of 300students,68% said they own an iPod and a smartphone. Compute a 97% confidence interval for the true percent of students who own an iPod and a smartphone.
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