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Chapter 8: Q. T8.7 (page 549)

A 90%confidence interval for the mean μ of a population is computed from a random sample and is found to be90±30. Which of the following could be the 95%confidence interval based on the same data?

a. 90±21

b. 90±30

c. 90±39

d. 90±70

e. Without knowing the sample size, any of the above answers could be the 95%confidence interval.

Short Answer

Expert verified

The required correct option is(e)

Step by step solution

01

Given information

Confidence interval =90±30

Confidence level=90%

02

The objective is to find out the 95%confidence interval using the same data

The width of the confidence interval is known to be proportional to the sample size. As a result, the width of the interval would become wider for the sample data at 95%confidence level. The sample size must be known in order to compute the confidence interval.

Therefore, the correct option is(e)

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Most popular questions from this chapter

Estimating BMI 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 μ in this population to within ±1 with 99% confidence?

Judy is interested in the reading level of a medical journal. She records the length of a random sample of100words. The histogram displays the distribution of word length for her sample. Determine if the Normal/Large Sample condition is met in this context.

Bone loss by nursing mothers Breast-feeding mothers secrete calcium into

their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breast-feeding. 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 percent change in BMC in the population of breast-feeding mothers.

b. Based on your interval from part (a), do these data give convincing evidence that

nursing mothers lose bone mineral, on average? Explain your answer.

More weight loss Refer to Exercise 6. Interpret the confidence level.

You want to compute a 90%confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30. What critical value should you use for this interval?

a. 1.645

b. 1.699

c. 1.697

d. 1.96

e. 2.045
See all solutions

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