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Chapter 8: Q.3.3 (page 511)

Construct a 95% confidence interval forM. Show your method

Short Answer

Expert verified

The obtained confidence interval is (22.338,29.962)

Step by step solution

01

Given information

Given in the question that, Biologists studying the healing of skin wounds measured the rate at which new cells closed a cut made in the skin of an anesthetized newt. Here are data from a random sample of 18newts, measured in micrometers (millionths of a meter) per hour:

20292734402228143526351230231811222333

02

Explanation

The given dataset is

29
27
34
40
22
28
14
35
36
35
12
30
23
18
11
2223
33

The formula to compute the confidence interval is:

x¯-ta2×sn<μ<x¯+ta2×sn

The output obtained using Ti-83calculator is:

Thus, the obtained confidence interval is(22.338,29.962).

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Most popular questions from this chapter

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.

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

64. Vitamin C content Several years ago, the U.S. Agency for International Development provided 238,300 metric tons of corn-soy blend (CSB) for
emergency relief in countries throughout the world. CSB is a highly nutritious, low-cost fortified food. As part of a study to evaluate appropriate vitamin C levels in this food, measurements were taken on samples of CSB produced in a factory. The following data are the amounts of vitamin C,

measured in milligrams per 100grams (mg/100 g) of blend, for a random sample of size8 from one production run:
2631232211221431
Construct and interpret a95%confidence interval for the mean amount of vitamin C M in the CSB from this production run.

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4inches long and 1.5inches square? A random sample of 20similar pieces of Douglas fir from a large batch was selected for a science class. The Fathom boxplot below shows the class’s data. Explain why it would not be wise to use a one-sample t interval to estimate the population meanμ.

The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI M in this population to within ±1vwith 99% confidence? Show your work.
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