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Chapter 7: Q4 (page 351)

LeftiesThere have been several studies conducted in an attempt to identify ways in which left-handed people are different from those who are right handed. Assume that you want to estimate the mean IQ of all left-handed adults. How many random left-handed adults must be tested in order to be 99% confident that the mean IQ of the sample group is within four IQ points of the mean IQ of all left-handed adults? Assume that is known to be 15.

Short Answer

Expert verified

The number of left-handed adults that must be tested in order to be 99% confident that the mean IQ of the sample group is within four IQ points of the mean IQ of all left-handed adults is 94.

Step by step solution

01

Given information

The level of confidence is 99%.

The margin of error is E=4.

The population standard deviation is σ=15.

02

Compute the sample size

The level of confidence is 99%, which implies that the level of significance is 0.01.

From the Z table, the critical value at 0.01 level of significance is 2.5758.

The number of left-handed adults that must be tested in order to be 99% confidentthat the mean IQ of the sample group is within four IQ points of the mean IQ of all left-handed adults is computed as follows:

n=(zα2×σ)2E2=2.57582×15242=93.301≈94

Therefore, the number ofleft-handed adults that must be tested is 94.

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Most popular questions from this chapter

Using Appendix B Data Sets. In Exercises 29 and 30, use the indicated data set in Appendix B. Green M&Ms Data Set 27 “M&M Weights” in Appendix B includes data from 100 M&M plain candies, and 19 of them are green. The Mars candy company claims that 16% of its M&M plain candies are green. Use the sample data to construct a 95% confidence interval estimate of the percentage of green M&Ms. What do you conclude about the claim of 16%?

Chickenpox : You plan to conduct a survey to estimate the percentage of adults who have had chickenpox. Find the number of people who must be surveyed if you want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults.

a. Assume that nothing is known about the prevalence of chickenpox.

b. Assume that about 95% of adults have had chickenpox.

c. Does the added knowledge in part (b) have much of an effect on the sample size?

Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7UP, A&W root Beer, Cherry Coke, …TaB). Use a confidence interval 99%. Does the confidence interval give us good information about the population of all cans of the same 20 brands that are consumed? Does the sample appear to be from a normally distributed population? If not, how are the results affected?

0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47

In Exercises 1–3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 “Airport Data Speeds” in Appendix B. The confidence level of 95% was used.

Degrees of Freedom

a. What is the number of degrees of freedom that should be used for finding the critical value tα2?

b. Find the critical value tα2corresponding to a 95% confidence level.

c. Give a brief general description of the number of degrees of freedom.

Finding Sample Size Instead of using Table 7-2 for determining the sample size required to estimate a population standard deviation s, the following formula can be used

n=12zα2d2

where corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95% confident that s is within 15% of the value of s, use zα2=1.96 and d = 0.15 to get a sample size of n = 86. Find the sample size required to estimate s, assuming that we want 98% confidence that s is within 15% of σ.
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