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Chapter 8: Q.8.3 (page 452)

Table 8.2shows a different random sampling of 20cell phone models. Use this data to calculate a 93% confidence interval for the true mean SAR for cellphones certified for use in the United States. As previously, assume that the population standard deviation is 蟽= 0.337.

Phone ModelSAR Phone ModelSAR
Blackberry pearl81201.48
Nokia E71x1.53
HTC Evo Design 4G0.8
Nokia N750.68
HTC Freestyle1.15
Nokia N791.4
LG Ally1.36
Sagem Puma1.24
LG Fathom0.77
Samsung Fascinate0.57
LG Optimus Vu0.462
Samsung Infuse 4G
0.2
Motorola Cliq XT1.36
Samsung Nexus S0.51
Motorola Droid pro1.39
Samsung Replenish0.3
Motorola Droid Razr M1.3
Sony W518a walkman0.73
Nokia 7705Twist0.7
ZTE C79 0.869

Short Answer

Expert verified

We estimate with 93% confidence that the true population mean is between 0.7996and 1.0724

Step by step solution

01

Given Information

Given in the question, the value as

The population standard deviation is 蟽= 0.337.

02

Explanation

If x-is the sample mean of a random sample of size n from a normal population with unknown variance 蟽2, a 100(1-伪) % Cl on 渭is given by

x炉鈭�z伪2蟽n鈮�渭鈮�x炉+z伪2蟽n (1)

wherez伪2is the upper100伪2percentage point of the standard normal distribution.

We know that standard deviation is蟽=0.337, a random samplen=20and a sample mean

x炉=1.48+0.8+鈰�+0.86920=0.936

We need to find a 93% confidence interval estimate for the population mean. Therefore,

伪2=1鈭�0.932=0.035鈬�z伪2=z0.035=1.81 (2)

03

Explanation

The earlier implication was obtained on a probability table for the standard normal distribution.

From equations (1) and (2) we get

0.936鈭�1.810.33720鈮�渭鈮�0.936+1.810.33720

Therefore,93%Clfor渭is

0.7996鈮�渭鈮�1.0724

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Most popular questions from this chapter

The data in the Table are the result of a random survey of 39national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X=the number of colors on a national flag.

XFreq.11273184756

Construct a 95%confidence interval for the true mean number of colors on national flags.

The 95%confidence interval is_____.

In words, define the random variable X.

What will happen to the confidence interval obtained, if 500 newborn elephants are weighed instead of 50? 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.

Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners, 250 identified themselves as midlevel managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred trucks, 54% of mid-level managers preferred trucks, and 26% of executives preferred trucks.

Suppose we want to lower the sampling error. What is one way to accomplish that?
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