Question

Answer the following about T-Test & T-distributions:

1. Which of the following statements related to the t-distribution is not true?

Select one:

a. Since the population standard deviation is usually unknown, the standard error of the sample mean is estimated using the sample standard deviation as an estimator for the population standard deviation. The formula is s/sqrt(n).

b. The population must be t-distributed in order to use the t-distribution.

c. Like the Normal distribution, the t-distribution is symmetric and unimodal.

d. The t-distribution is generally bell-shaped, and the shape of the t-distribution gets closer to the shape of the Normal distribution as sample size increases.

As sample size increases, and all summary statistics remain the same, what will happen to the test statistics for the z-test and the t-test?

Select one:

a. They will both increase in magnitude

b. They will not change

c. The t-statistic will increase in magnitude, the z-statistic will not

d. They will both decrease in magnitude

e. The z-statistic will increase in magnitude, the t-statistic will not

f. None of these are true.

Note: I know for question #2 that it is not f. and for #1 I think that the answer is b?

Answer 1

1)

we use t distribution when given data is normally distributed and sample size is small or population standard deviation is unknown and we use sample s.d as the best estimate

As we use t distribution when data is normally distributed so, it is symmetrical like normal distribution

And yes as the sample size increases it approaches the standard normal distribution

So, only false statement is

b. The population must be t-distributed in order to use the t-distribution

2)

Test statistics z or t = (sample mean - claimed.mean)/(s.d/√n)

Or ((sample mean - claimed mean)*√n)/(s.d)

So, test statistics is directly proportional to the sample size n

So, answer is

a. They will both increase in magnitude