Use the Following Information to Answer the Question

question 7

Multiple Choice

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-Suppose the process of taking random samples of size 30 from the 40- 44 age group is repeated 200 times and a histogram of the 200 sample means is created. Which statement best describes the shape of the histogram?

• A)The histogram will be roughly bell- shaped.
• B)The histogram will be unimodal.
• C)The histogram will be roughly symmetrical.
• D)All of these statements are true.

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Definitions:

Sampling Frame

The list or set from which a sample is drawn, representing the population from which researchers intend to collect data.

Population Size

The total number of individuals or units in the group that is the subject of statistical analysis.

Average Age

The mean value of the ages of individuals in a specific group or population, calculated by dividing the sum of all ages by the number of individuals.

Random

In statistical terms, a process or selection that ensures each item or person has an equal chance of being chosen, free from bias.