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Chapter 8: Q. R8.7 (page 548)

Good wood? A lab supply company sells pieces of Douglas fir 4 inches long and

1.5 inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a distribution with standard deviation 3000 pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000 pounds with 95% confidence. How large a sample is needed?

Short Answer

Expert verified

The required sample is35

Step by step solution

01

Given information

Standard deviation(σ)=3000

Confidence level=95%

Margin of error(E)=1000

02

The objective is to find out the sample size to have the margin error within 1000pounds at 95%the confidence level.

We know,

The formula to compute the sample size is:

n=zα2×σE2

According to the standard normal table, the value of za2corresponding to the 95%confidence level is1.96

The sample size can be calculated as:

n=zα2×σE2=1.96×300010002=34.5744≈35

Therefore, the sample size is35

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Most popular questions from this chapter

Fruit fly thorax lengths Fruit flies are used frequently in genetic research because of their quick reproductive cycle. The length of the thorax (in millimeters) was measured for each fly in a random sample of 49male fruit flies. The mean length was x¯=0.8004mm, with a standard deviation of sX=0.0782mmmm. Construct and interpret a 90%confidence interval for the true mean thorax length of a male fruit fly.

A 90%confidence interval for the mean μ of a population is computed from a random sample and is found to be90±30. Which of the following could be the 95%confidence interval based on the same data?

a. 90±21

b. 90±30

c. 90±39

d. 90±70

e. Without knowing the sample size, any of the above answers could be the 95%confidence interval.

You have an SRS of 23observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98%confidence interval for the mean of the population?

a. 2.177

b. 2.183

c. 2.326

d. 2.500

e. 2.508

Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs

of shoes that female students have by estimating the population standard deviation σ.

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