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Chapter 8: Q. T8.8 (page 549)

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of at most \(2. Based on last year’s book sales, we estimate that the standard deviation of the amount spent will be close to \)30. The number of observations required is closest to which of the following?

a. 25

b.30

c. 225

d. 609

e. 865

Short Answer

Expert verified

The required number of observations is 25

The correct option is(a)

Step by step solution

01

Given information

Standard deviation (σ)=30

Confidence level =90%

Margin of error(E)=2

02

The objective is to find out the number of observations.

We know,

The formula to compute the sample size is:

n=zα2×σE2

The standard normal table yields the value of za2corresponding to a 90%confidence level of1.645.

The total number of observations can be calculated as follows:

n=zα2×σE2=1.645×3022=24.675≈25

The sample size is 25

Therefore, the correct option is(a)

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Most popular questions from this chapter

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 μ at a 99% confidence level based on an SRS of size 58

The 10%condition When constructing a confidence interval for a population proportion, we check that the sample size is less than 10%of the population size.

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Do you go to church? The Gallup Poll plans to ask a random sample of adults

whether they attended a religious service in the last 7 days. How large a sample would be required to obtain a margin of error of at most 0.01 in a 99% confidence interval for the population proportion who would say that they attended a religious service?

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

More income The 2015American Community Survey estimated the median household income for each state. According to ACS, the 90%confidence interval for the 2015

median household income in New Jersey is \(72,222±\)610.

a. Interpret the confidence interval.

b. Interpret the confidence level.
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