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Chapter 8: Q.9 (page 482)

How confident? The figure below shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for each sample. Which confidence level鈥�80%,90%,95%, or 99%鈥� do you think was used? Explain

Short Answer

Expert verified

The nearest confidence level is 80%.

Step by step solution

01

Given Information

The result of 25SRSs:

02

Explanation

The red lines under the curve represent the sample means that does not contain the true population mean 渭.

We note that there are 4out of the 25samples that do not contain the true proportion and thus 21out of the 25samples contain the true mean:

2125=0.84=84%

The nearest confidence level is 80%

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Most popular questions from this chapter

Teens" online profiles Describe a possible source of error that is not included in the margin of error for the 95% confidence interval in Exercise 36

Auto emissions Refer to Exercise 6. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals? (Use Figure 8.5, on page 474, as a model for your drawing.)

Bone loss by nursing mothers.: Breastfeeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone minerals. Researchers measured the per cent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breastfeeding. The mean change in BMC was 3.587%and the standard deviation was 2.506%.

(a) Construct and interpret a 99% confidence interval to estimate the mean per cent change in BMC in the population.

(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone minerals? Explain

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24laboratory rats. A 95%confidence interval for the mean blood cholesterol level Mis 80.2to 89.8. Which of the following would cause the most worry about the validity of this interval?

(a) There is a clear outlier in the data.

(b) A stemplot of the data shows a mild right skew.

(c) You do not know the population standard deviation S.

(d) The population distribution is not exactly Normal.

(e) None of these would be a problem because the t procedures are robust.

57. Critical values What critical value t* from Table B would you use for a confidence interval for the population mean in each of the following situations?
(a) A 95%confidence interval based on  n=10 observations.
(b) A 99%confidence interval from an SRS of 20 observations.

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