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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.

Short Answer

Expert verified

(a)The critical value is2.518

(b)The critical value is1.833

(c)The critical value is2.447

Step by step solution

01

part (a) Step 1: Given information

Given in the question that, 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. A 98% confidence interval based onn=22observations.

02

Part (a) Step 2: Explanation

Given:

Confidence level =98%

Sample size (n)=22

The level of significance is:

Level of significance

Level of significance=1-Confidence level

=1-0.98

=0.02

The degree of freedom is22-1=21

The critical value using standard normal table is calculated as:

localid="1649870225365" ta/2df=t0.02/2,21

=2.518

The critical value is2.518

03

part (b) Step 1: Given information

Given in the question that, 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 90%confidence interval from an SRS of10 observations.

04

Part (b) Step 2: Explanation

Given:

Confidence level =90%

Sample size (n)=10

The level of significance is:

Level of significance=1-Confidence level

=1-0.90

=0.10

The degree of freedom is 10-1=9

The critical value using standard normal table is calculated as:

ta/2df=t0.10/2,9

=1.833

The critical value is1.833.

05

part (c) step 1: Given information

Given in the question that, 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. (c) A95%confidence interval from a sample of size7.

06

Part (c) Step 2: Explanation

Given:

Confidence level =95%

Sample size (n)=7

The level of significance is:

Level of significance=1-Confidence level

=1-0.95

=0.05

The degree of freedom is7-1=6

The critical value using standard normal table is calculated as:

ta/22d=t0.05/2,6

=2.447

The critical value is2.447

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Most popular questions from this chapter

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%.

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A radio talk show host with a large audience is interested in the proportion pof adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100people who phoned in, 70answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

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I collect an SRS of size n from a population and compute a 95%confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level.

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(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.

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