Question

Miriam is using a one-sample t-test on the following group:

Subject #15: 6.5 hours
Subject #27: 5 hours
Subject #48: 6 hours
Subject #80: 7.5 hours
Subject #91: 5.5 hours

Select the two TRUE statements.

• a.)

  The t-distribution that Miriam uses is taller and has thinner tails than a normal distribution.

• b.)

  The value for the degrees of freedom for Miriam's sample population is five.

• c.)

  The t-distribution that Miriam uses is shorter and has thicker tails than a normal distribution.

• d.)

  Miriam needs to use a t-test when the standard deviation is known.

• e.)

  The value for the degrees of freedom for Miriam's sample population is four.

Answer 1

Here, the sample size (n) is 5 and hence, the degrees of freedom = n - 1 = 4. The t-test is used normally when the (population) standard deviation is unknown. The t distribution is similar to the normal distribution, but with fatter tails.
Hence, the two TRUE statements are:
The t-distribution that Miriam uses is shorter and has thicker tails than a normal distribution.
The value for the degrees of freedom for Miriam's sample population is four.