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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

On May 23,2013, Gallup reported that of the 1005people surveyed, 76%of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at 95%with a 卤3%margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and .

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the values.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience?

Using the same mean, standard deviation, and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?

If the Census wants to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make?

Suppose we have data from a sample. The sample mean is 15, and the error bound for the mean is 3.2. What is the confidence interval estimate for the population mean?

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_____.
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