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.
-Which of the following statements is not true about the t-distribution?
A) Like the normal distribution, the t-distribution is symmetric and unimodal.
B) For small sample sizes, the t-distribution has all the same properties of the normal curve.
C) Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation. The formula is
$$\mathrm { SE } _ { \text {est } } = \mathrm { s } / \sqrt { \mathrm { n } }$$
D) All of these statements about the t-distribution are true.

Question

Quizplus · Accepted Answer

The t-distribution differs from the normal distribution, especially for small sample sizes, as it has heavier tails, meaning it is more prone to producing values that fall far from its mean.

Use the Following Information to Answer the Question SEest =s/n\mathrm { SE } _ { \text {est } } = \mathrm { s } / \sqrt { \mathrm { n } }SEest ​=s/n​

Use the Following Information to Answer the Question $\mathrm { SE } _ { \text {est } } = \mathrm { s } / \sqrt { \mathrm { n } }$