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Chapter 8: Q 8.42 (page 330)

Suppose that you will be taking a random sample from a population and that you intend to find a 95%confidence interval for the population mean μ. Which sample size, 25or30 , will result in the confidence interval giving a more accurate estimate of μ?

Short Answer

Expert verified

Sample size of50will result in the confidence interval giving a more accurate estimate ofμ.

Step by step solution

01

Given Information

Given confidence level is 95%for a sample taken randomly from population. Two sample size of25and50are given.

02

Explanation

We know that sample size is increased and confidence level is constant, in results in decrease in margin of error. Hence, accuracy of confidence level estimation is increased.

Therefore as per the given data, sample size of 50will result in the confidence interval giving a more accurate estimate of μwhen compared to that of sample size50.

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Most popular questions from this chapter

For the one-mean t-interval procedure, express the formula for the endpoints of a confidence interval in the form.

A variable has a mean of 100 and a standard deviation of 16 Four observations of this variable have a mean of 108 and a sample standard deviation of 12 . Determine the observed value of the

a. standardized version of x¯.

b. studentized version of x¯.

Medical Marijuana. An issue with legalization of medical marijuana is "diversion," the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. Researchers S. Sautel et al. study the issue of diversion in the article "Medical Marijuana Use Among Adolescents in Substance Abuse Treatment" . The mean number of days that 120adolescents in substance abuse treatment used medical marijuana in the last six months was 102.72. Assume the population standard deviation is 32days.

a. Find a 95%confidence interval for the mean number of days, μ, of diverted medical marijuana use in the last 6 months of all adolescents in substance abuse treatment.

b. Repeat part (a) at a 90%confidence level.

c. Draw a graph similar to Fig. 8.6on page 326to display both confidence intervals.

d. Which confidence interval yields a more accurate estimate ofμ ? Explain your answer.

One-Sided One-Mean z-Intervals. Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for (1-α)-level confidence bounds for a population mean \(\mu\) :

- Lower confidence bound: x~-zσ·σ/n

- Upper confidence bound: x¯+zα·σ/n

Interpret the preceding formulas for lower and upper confidence bounds in words.

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a. Obtain a normal probability plot, boxplot, and histogram of the data.

b. Is it reasonable to apply the t--interval procedure to the data? Explain your answer.

c. If you answered "yes" to part (b), find a 95%confidence interval for men's average forearm length Interpret your result.
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