Determine the critical 𝑡 value for a 99% confidence level

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ANSWER ALL QUESTIONS

Topic – 7.2 (Estimating a Population Mean)

Complete this quiz on your own paper. Then scan it as a pdf and submit it to Blackboard.

1. [2 points] Suppose you select 25 Douglas College students at random and determine their ages.

Using those 25 numbers, you calculate the sample mean, 𝑋̅ = 21.5 years, and sample standard deviation, 𝑠 = 3.1 years.

The confidence interval for 𝜇, the population mean age of Douglas College students, at confidence level 1 − 𝛼, is:

(𝑋̅ − 𝑡𝛼/2 ⋅ 𝑠 √𝑛 ,𝑋̅ + 𝑡𝛼/2 ⋅ 𝑠 √𝑛 )

a. Determine the critical 𝑡 value for a 99% confidence level.

b. Find the 99% confidence interval for 𝜇. 2. [2 points] Suppose that you are unhappy with this confidence interval because the margin of error, 𝐸, is too large. Which of the following would decrease the margin of error?

Pick one and explain why it decreases the margin of error.

i. Use a smaller 𝑛.

ii. Use a lower 𝛼

iii. Use a lower confidence level, (i.e., lower 1 − 𝛼)

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