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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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State the estimated distribution of P鈥�.Construct a 92%Confidence Interval for the true proportion of girls in the ages 8to12beginning ice-skating classes at the Ice Chalet.

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

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In complete sentences, explain why the confidence interval in Exercise 8.17 is larger than in Exercise 8.18.

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.

a. What is the probability distribution for X?

b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X.

c. Use your calculator to find the probability that DeAndre scored with 60 of these shots.

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