22. A study of the ages of motorcyclists killed in crashes involves the random s

Question

22. A study of the ages of motorcyclists killed in crashes involves the random selection of 134 drivers with a mean of 33 92 years. Assuming that -82 years, construct and interpret a 99% confidence interval estimate of the mean age of all motorcyclists killed in crashes. 13 Click here to view page 1 of the standard normal distribution table 14 Click here to view page 2 of the standard normal distribution table. 15 What is the 99% confidence interval for the population mean ? He (Round to two decimal places as needed.) Notice that the confidence interval limits do not include ages below 20 years. What does this mean? 0 A. B. ° C. 0 D. The mean age of the population will most likely not be less than 20 years old. The mean age of the population will never be less than 20 years old. Motorcyclists under the age of 20 never die in crashes The mean age of the sample will most likely not be less than 20 years old. 13: Critical t values

Explanation / Answer

Solution:

We are given

Sample size = n = 134

Sample Mean = Xbar = 33.92

Population standard deviation = = 8.2

The confidence interval formula is given as below:

Confidence interval = Xbar -/+ Z*/sqrt(n)

We use Z (normal) distribution because we are given a value for population standard deviation.

Confidence level = c = 99% = 0.99, so, = 1 – c = 1 – 0.99 = 0.01, so /2 = 0.01/2 = 0.005

Critical value = Z/2 = 2.5758

Confidence interval = 33.92 -/+ 2.5758*8.2/sqrt(134)

Confidence interval = 33.92 -/+ 1.8246

Lower limit = 33.92 – 1.8246 = 32.0954

Upper limit = 33.92 + 1.8246 = 35.7446

Confidence interval = (32.0954, 35.7446)

32.10 < µ < 35.74

Notice that the confidence interval limits do not include ages below 20 years. What does this mean?

Answer:

(Confidence interval provides the bound for population parameter and not a sample statistic.)

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