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Chapter 8: Q 8.41 (page 330)

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 ?

Short Answer

Expert verified

Confidence level of 95%will estimate population mean more precisely.

Step by step solution

01

Given Information

Data is obtained by taking a random sample from population. Two confidence intervals of value95%,97%are available to measure population mean.

02

Explanation

As we know that larger confidence level results in larger confidence interval of μ.

Hence, for 99%confidence interval, we will obtain μof smaller length as compared to that of 99%.

Therefore the estimation of population mean is better in case of 95%as compared to99%.

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Most popular questions from this chapter

Toxic Mushrooms? Refer to Exercise 8.71

a. Determine and interpret a 99% lower confidence bound for the mean cadmium level of all Boletus Pinicola mushrooms.

b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interval found in Exercise 8.71

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.

Bottlenose Dolphins. The webpage "Bottlenose Dolphin" produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of 50adult bottlenose dolphins have a mean length of 12.04ftwith a standard deviation of 1.03ft Find and interpret a 90% confidence interval for the mean length of all adult bottlenose dolphins.

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.

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

  • Lower confidence bound: x¯-tα-s/π
  • Upper confidence bound: x^+tα·s/n

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