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Chapter 8: Q 8.3RP. (page 346)

Must the variable under consideration be normally distributed for you to use the z-interval procedure or t-interval procedure? Explain your answer.

Short Answer

Expert verified

No.

Step by step solution

01

Explanation

No,

The z-interval or t-interval approach can be used to find the confidence interval of a population mean even if the variable under investigation is not normally distributed.

Because of the following conditions are met, we can apply the z-interval or t-interval technique for non-normally distributed variables.

  • Large sample i.e, sample size >30
  • The variable in question is near to being normally distributed, and there are no outliers in the sample data.

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Most popular questions from this chapter

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 distribution of the variable under consideration is highly skewed, and the sample size is 20.

State True or False. Give Reasons for your answers.

The confidence interval can be obtained if you know only the margin of error and the sample mean.

"Chips Ahoy! 1,000 Chips Challenge." As reported by B. Warner and J. Rutledge in the paper "Checking the Chips Ahoy! Guarantee" (Chanee, Vol. 12. Issue 1. pp. 10-14), a random sample of forty-two 18-ounce bags of Chips Ahoy! cookies yielded a mean of 1261.6 chips per bag with a standard deviation of 117.6 chips per bug.

a. Determine a 95% confidence interval for the mean number of chips per bag for all 18-ounce bags of Chips Ahoy! cookies, and interpret your result in words.

b. Can you conclude that the average 18-ounce bag of Chips Ahoy! cookies contain at least 1000 chocolate chips? Explain your answer.

What is a confidence interval estimate of a parameter? Why is such an estimate superior to a point estimate?

Political Prisoners. A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper "Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of Mental Defeat. Alienation, and Perceived Permanent Change". According to the article. the mean duration of imprisonment for 32 patients with chronic PTSD was 33.4months. Assuming that σ=42months, determine a 95%confidence interval for the mean duration of imprisonment,μ. of all East German political prisoners with chronic PTSD. Interpret your answer in words.
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