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)

The use of student-test implies:

The solution is:

a) t(s) will be the same

b) t(s) will decrease

c) t(s) will be the same

d) t(s) will decrease

a) To calculate t(s), we use the equation:

t(s) = (μ  -  μ₀)/s/√n         (1)

where:

μ is sample mean

μ₀ is the population mean

s is sample standard deviation

n sample size

As  we can see, t(s) does not depend on the confidence level (α), therefore changing confidence level,  would not affect t(s) value

b) Increasing s²,  will make t(s) decrease as from equation (1)

c) As explained in letter a), t(s) does not depend on α. Hence, changing α, would not affect the value of t(s)

d) If the sample size n  decrease t(s) will decrease

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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.