Question

1

Identify each of the following statements as either TRUE or FALSE. a) Click for List The t distribution tends toward the standard normal distribution as the degrees of freedom increase. b) Click for List The t distribution has more area in the tails than the standard normal distribution. Click for List If I is a random variable with a t distribution, then P(T<0) = 0.5. Click for List If we wish to carry out inference procedures on the mean of a normally distributed population where sigma is known, we should use the t distribution. e) Click for List Random variables with a t distribution cannot take on negative values.

Answer 1

(a) TRUE

>> With increase in degrees of freedom, the sample size increases. When the sample size increases, the t distribution tends toward the standard normal distribution.

(b) TRUE

>> The t-distribution is bell-shaped like the normal distribution, but has more area in the tails, meaning that it is more prone to producing values that fall far from its mean.

(c) TRUE

>> Both left and right sides of the mean have equal probability of 0.5 in t distribution, meaning that P(T<0) = P(T>0) = 0.5.

(d) FALSE

>> For normally distributed population, when sigma (population standard deviation) is known, we use standard normal distribution to inference the mean.

(e) FALSE

>> Random variables with t distribution can take both positive or negative values.