Statistics 1 Class Recitation

Who discovered the t-distribution?

• William S. Gosset

• William Shakespeare

• William P. Wallace

• William Bowery

Answer explanation

Gosset is a quality control engineer in Guiness Brewery. He observed that the samples of stout that he rejected turns out to be accepted by the laboratory. After a thorough study of this problem, Gosset found out that the shape of the sampling distribution changes based on the number of samples. This model is a family of curves called t – distribution.

True or False. William S. Gosset used "student" as a pseudonym because he was not allowed by the Guinnes Brewery to publish under his name.

• True

• False

Answer explanation

True.It is written in the Guiness Brewery company policy.

When do we use t-distribution? Note: You may choose more than 1 answer.

• when the population standard deviation is unknown

• when the distribution is not normal

• when the standard deviation is equal to 0.

What is the shape of t-distribution?

• Bell-shaped and symmetric wrt center

• skewed to the left or negatively skewed

• skewed to the right or positively skewed

• uniform

Answer explanation

(see image)

Which has fatter tails?

• t-distribution

• normal distribution

• standard normal distribution

• chi-square distribution

Answer explanation

(see image)

True or False. A t-distribution is a family of curves that varies depending on its mean.

• True

• False

Answer explanation

False. A t-distribution depends on its sample size or degrees of freedom.

What is the degrees of freedom of the t-distribution if its sample size is 8?

• 7

• 6

• 8

• 9

Fill in the blank. A t-distribution which has a d.f. of 15 has a _____ tail than a t-distribution which has a d.f. of 2.

• heavier

• lighter

• longer

• shorter

Answer explanation

Heavier. The degrees of freedom indicate the tail heaviness of a t – distribution.

True or False. The t-distribution becomes similar to the standard normal distribution as sample size becomes larger.

• True

• False

Answer explanation

True. As n increases, the t-distribution will approach the standard normal distribution.

Fill in the blank. As the d.f. ______, the t-distribution approaches the standard normal distribution

• increases

• decreases

• stays the same

Answer explanation

Increases. The t-distribution becomes similar to the standard normal distribution as sample size becomes larger.