Question

Suppose you conduct a hypothesis test about a population mean when the standard deviation is unknown by calculating a t statistic and determining whether to reject the null hypothesis. Assume that your t statistic is a positive value and that you will reject the null hypothesis when t is very large. For each of the potential changes to the components of your study design or the results listed below, determine the change to the t statistic.
a. A switch from using a two-tailed test to a one-tailed test
b. An increase in the sample variance (s^2)
c. An increase In the significance level (such as using α= 0.05 instead of σ= 0.02)
d. A decrease in the sample Size (n)

Answer 1

Answer:

a. remain the same

b. decrease

c. remain the same

d. t decreases

the answers are in bold letters under each question. Thank you

Step-by-step explanation:

a. A switch from using a two-tailed test to a one-tailed test

A switch from 2 tailed test to one tailed test will have t statistic remain the same. This does not change the value of t statistic

b. An increase in the sample variance (s^2)

when sample variance s^2 is increased, we will have it that standard error has increased. therefore t statistic will decrease

c. An increase In the significance level (such as using α= 0.05 instead of σ= 0.02)

t statistics will remain the same. this is due to the fact that significance level is not a part of the t statistics formula.

d. A decrease in the sample Size (n)

when sample size is decreased, standard error will increase. therefore t statistic will decrease.