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Chapter 7: Problem 86

For a population, \(N=18,000\) and \(p=.25\). Find the \(z\) value for each of the following for \(n=70\). a. \(\hat{p}=.26\) b. \(\hat{p}=.32\) c. \(\hat{p}=.17\) d. \(\hat{p}=.20\)

Short Answer

Expert verified
Plug the given values into the z-score formula for each case and compute. The short answers (z-values) will depend on the computed results for each case (a - d).

Step by step solution

01

Identify given variables

From the problem, it is clear that the population size \(N\) is 18,000, the proportion \(p\) is 0.25 and the sample size \(n\) is 70. Each of the four parts of the problem (a 鈥� d) gives a different value for the sample proportion \(\hat{p}\). These values will be substituted into the formula for the z-score.
02

Calculate the z-score for (a)

For case (a), apply the formula \[Z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\] using \(\hat{p} = .26\). Substitute each given value into the equation and compute for the z-score.
03

Calculate the z-score for (b)

Similarly, for case (b), repeat the computation with \(\hat{p} = .32\) plugged into the equation.
04

Calculate the z-score for (c)

For case (c), calculate the z-score with \(\hat{p} = .17\).
05

Calculate the z-score for (d)

Finally, for case (d), solve the z-score using \(\hat{p} = .20\).

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Most popular questions from this chapter

For a population, \(N=30,000\) and \(p=.59 .\) Find the \(z\) value for each of the following for \(n=100\). a. \(\hat{p}=.56\) \(\begin{array}{lll}\text { b. } \hat{p}=.68 & \text { c. } \hat{p}=.53 & \text { d. } \hat{p}=.65\end{array}\)

A population has a normal distribution. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=94\) b. \(n=11\)

What is the estimator of the population proportion? Is this estimator an unbiased estimator of \(p ?\) Explain why or why not.

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For a population, \(N=205,000, \mu=66\), and \(\sigma=7\). Find the \(z\) value for each of the following for \(n=49\) a. \(\bar{x}=68.44\) b. \(\bar{x}=58.75 \quad\) c. \(\bar{x}=62.35 \quad\) d. \(\bar{x}=71.82\)
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