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Chapter 8: Q.9 (page 523)

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.

Short Answer

Expert verified

The sample size is35

Step by step solution

01

Step-1 Given Information

Given in the question that ,

Margin of error(E)=1000

Standard deviationσ=3000

Confidence level=95%we have to find How large a sample is needed.

02

Step-2 Explanation

The value of zα2corresponding to 95%confidence level 1.96which is obtained from standard normal table.

the sample size can be calculated as follows:

Samplesize(n)=zα×σ2E2

=1.96×300010002

≈35

Thus,the sample size is35

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Most popular questions from this chapter

In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.

1. An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."

2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

Explain briefly why each of the three conditions—Random, Normal, and Independent—is important when constructing a confidence interval.

It’s critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

(a) Estimating a population proportion p at a 94%confidence level based on an SRS of size 125.

(b) Estimating a population mean M at a 99%confidence level based on an SRS of size 58.

56. The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points.
How large a sample of high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence? Show your work.

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

(a) How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90% confidence? Answer this question using the 75% estimate as to the guessed value for p∧.

(b) Answer the question in part (a) again, but this time use the conservative guess p∧=0.5. By how much do the two sample sizes differ?
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