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Chapter 8: Q.8.7 (page 456)

The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?

Short Answer

Expert verified

The required sample size is35

Step by step solution

01

Given Information

It is given that,

s =3

EBM = 1

and the confidence level is 95%

02

Explanation

If x-is used as an estimate of 渭, we can be 100(1-伪) % confident that the error bound EBM when the sample size is

n=(z伪2蟽EBM)2 (1)

We know that

1. standard deviation is s= 3

2. the error bound is EBM =1

3. and the confidence level is 95%

03

The required sample size

Therefore,

伪2=1鈭�0.952=0.025鈬�z0.025=1.96

Then, from Equation (1) is

n=(1.96脳31)2=34.57

and because n must be an integer,the required sample size is

n=35

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Most popular questions from this chapter

A sample of 20heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2pounds with a standard deviation of 0.1pounds. The population standard deviation is known to be 0.2pounds.

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The average height of young adult males has a normal distribution with a standard deviation of 2.5 inches. You want to estimate the mean height of students at your college or university to within one inch with 93 per cent confidence. How many male students must you measure?

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points.

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d. Find the probability that DeAndre scored with more than 50 of these shots
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