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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

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?

A telephone poll of 1000adult Americans was reported in an issue of Time Magazine. Another question in the poll was 鈥淸How much are] you worried about the quality of education in our schools?鈥� Sixty-three percent responded 鈥渁 lot鈥�. We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

a. Define the random variables Xand P鈥�in words.

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

c. Construct a 95%confidence interval for the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. The sampling error given by Yankelevich Partners, Inc. (which conducted the poll) is 卤3%. In one to three complete sentences, explain what the 卤3% represents.

Define the random variablesX andx{"x":[[179,180,181,183,186,189,193,196,198,200,202,204,205,207,208,210,211,212,213,214,214,215,215,215,215,215,215,214,212,211,209,207,206,204,203,201,199,198,197,195,194,193,192,191],[226,225,224,221,219,218,217,215,214,213,213,212,212,211,211,211,211,211,211,212,213,214,216,217,220,223,225,227,229,232,233,235,236,238,239,240,241,242,242,243],[164,165,168,176,181,187,192,197,202,205,207,212,215,216,218,219,220,221,222]],"y":[[101,100,100,99,97,96,96,96,96,96,96,97,98,100,100,102,104,105,107,108,109,111,112,113,115,117,119,121,123,124,125,127,127,128,128,129,129,129,129,129,129,129,128,128],[88,89,90,93,95,97,98,100,101,103,104,104,105,107,108,109,110,111,113,114,114,115,116,118,119,120,121,121,121,121,121,121,121,121,120,120,120,120,119,119],[84,84,83,81,80,78,77,77,76,76,75,75,74,73,73,73,72,72,72]],"t":[[0,334,339,357,374,390,408,424,440,457,473,490,506,523,540,557,574,590,606,623,640,657,675,689,706,724,740,756,774,789,806,823,840,857,873,890,907,923,940,957,974,990,1006,1023],[2075,2299,2306,2324,2340,2356,2373,2389,2406,2423,2443,2458,2473,2490,2508,2523,2551,2590,2606,2623,2640,2656,2674,2690,2707,2723,2740,2756,2772,2789,2806,2823,2840,2856,2873,2890,2907,2956,2973,2989],[4121,4332,4340,4356,4373,4389,4406,4423,4440,4456,4473,4489,4506,4523,4539,4557,4573,4598,4656]],"version":"2.0.0"} in words.

124. Refer to Exercise 8.123. Another question in the poll was "[How much are) you worried about the quality of education in our schools?" Sixty-three percent responded "a lot". We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

XandP'

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

c. Construct a 95% confidence interval for the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. The sampling error given by Yanklovich Partners, Inc. (which conducted the poll) is 卤3%. In one to three complete sentences, explain what the 卤3% represents.

Define the random variable X in words.
See all solutions

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