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Chapter 8: Q 62. (page 541)

Critical values What critical value t*from Table B should be used for a confidence interval for the population mean in each of the following situations?

a. A 90% confidence interval based on n=12 randomly selected observations

b. A 95% confidence interval from an SRS of 30 observations

c. A 99% confidence interval based on a random sample of size 58

Short Answer

Expert verified

a. The critical value is 1.796.

b. The critical value is 2.045.

c. The critical value is2.678.

Step by step solution

01

Part (a) Step 1: Given Information

It is given that n=12

Confidence Level=0.90

02

Part (a) Step 2: Calculation

Degree of freedom is calculated as:

df=n-1=12-1=11

Level of Significance, a=0.10

EXCEL formula =TINV(0.1,11)gives

t11,a/2=1.796

The critical value is1.796

03

Part (b) Step 1: Given Information

It is given that n=30

Confidence Level=0.95

04

Part (b) Step 2: Calculation

Degree of freedom is calculated as:

df=n-1=30-1=29

Level of significance, a=0.05

EXCEL formula =TINV(0.05,29)gives

t11,a/2=1.045

The critical value is1.045

05

Part (c) Step 1: Given Information

It is given that n=58

Confidence Level0.999

06

Part (c) Step 2: Calculation

Degree of freedom is df=n-1=58-1=57

Level of Significance is a=0.01

EXCEL formula =TINV(0.01,57)gives

t11,a/2=2.678

The critical value is2.678

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Most popular questions from this chapter

More cheating Refer to Exercise 36. Calculate and interpret the standard error of p^for these data.

One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that

a. zcan be used only for large samples.

b. zrequires that you know the population standard deviation 蟽.

c. z requires that you can regard your data as an SRS from the population.

d. z requires that the sample size is less than 10% of the population size.

e. a z critical value will lead to a wider interval than a t critical value.

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 渭 in this population to within 卤1 with 99% confidence?

A newspaper reporter asked an SRS of 100residents in a large city for their opinion about the mayor鈥檚 job performance. Using the results from the sample, the C%confidence interval for the proportion of all residents in the city who approve of the mayor鈥檚 job performance is 0.565to0.695. What is the value of C?

a. 82

b. 86

c. 90

d. 95

e. 99

The Large Counts condition When constructing a confidence interval for a population proportion, we check that both np鈭�andn1-p鈭�are at least 10

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?
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