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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

A confidence interval for a population mean has a length of 162.6.

a. Determine the margin of error.

b. If the sample mean is 643.1, determine the confidence interval.

c. Construct a graph that illustrates your results.

The value of a statistic used to estimate a parameter is called a ______ of the parameter.

Table IV in Appendix A contains degrees of freedom from I to 75 consecutively but then contains only selected degrees of freedom.

a. Why couldn't we provide entries for all possible degrees of freedom?

b. Why did we construct the table so that consecutive entries appear for smaller degrees of freedom but that only selected entries occur for larger degrees of freedom?

c. If you had only Table IV, what value would you use for t0 os with df =87 with df=125? with df=650? with df=3000 ? Explain your answers.

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, 渭, 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 of渭 ? Explain your answer.

The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
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