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Chapter 8: Q 8.37 (page 331)

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The sample data contain no outliers, the variable under consideration is roughly normally distributed, and the sample size is 20.

Short Answer

Expert verified

The z-interval procedure to obtain a confidence interval for the population mean is reasonable.

Step by step solution

01

Given Information

The variable under consideration is roughly normally distributed. The sample data contains no outliers.

02

Conditions to use zinterval procedure

The conditions are:

  • Small Sample Size: When sample size is n<15, procedure is used if the variable is normally distributed and very close to being normally distributed.
  • Moderate Sample Size: When sample size is between 15-30, the variable is far from being normally distributed and no outlier in the data.
  • Large Sample Size: When the sample size is greater than 30, it is used without restrictions.
03

Explanation

Sample size is 20.

It lies between 15-30.

Therefore,zinterval procedure to obtain a confidence interval for the population mean is reasonable.

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Most popular questions from this chapter

Suppose that you have obtained data by taking a random sample from a population and that you intend to find a confidence interval for the population mean, μ. Which confidence level, 95% or 99%, will result in the confidence interval giving a more accurate estimate of μ ?

Assume that the population standard deviation is known and decide weather use of the zinterval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The variable under consideration is very close to being normally distributed, and the sample size is75.

American Alligators. Refer to Exercise 8.78.

a. Determine the margin of error for the 95%confidence interval.

b. Determine the margin of error for the 99%confidence interval.

c. Compare the margins of error found in parts (a) and (b).

d. What principle is being illustrated?

Digital Viewing Times. Refer to Exercise 8.130

a. Find and interpret a 90%lower confidence bound for last year's mean time spent per day with digital media by American adults.

b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interval found in Exercise 8.130.

Toxic Mushrooms?Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5part per million (ppm). M. Melgar et al. measured the cadmium levels in a random sample of the edible mushroom Bolefus pinicola and published the results in the paper "Influence of Some Factors in Toxicity and Accumulation of Cd from Edible Wild Macrofungi in NW Spain (Journal of Envionmental Science and Health. Here are the data obtained by the researchers.

Find and interpret a 99%confidence interval for the mean cadmium level of all Boletus pinicola mushrooms. Assume a population standard deviation of cadmium levels in Bolefus pinicola mushrooms of 0.37ppm.
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