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.
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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