3) A random variable (t) follows the Student’s t-distribution with the degrees o

Question

3) A random variable (t) follows the Student’s t-distribution with the degrees of freedom equal to 10.

a. Given that the degrees of freedom equals 10, what value can we infer about the sample size?

b. What is the probability that t is greater than 1.55 for a two-tailed test? Use Table D (p. 307), and draw the probability underneath the curve before you make your answer.

c. In order to obtain a confidence interval at a 95% confidence level for a two-tailed test, what value of t should be used as the tcrit?

d. In order to obtain a confidence interval at a 90% confidence level for a one-tailed test (assume it’s a positive test), what value of t should be used as the tcrit?

Explanation / Answer

a.
degrees of freedom = n - 1 = 10 , n = 11
c.
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.228
since our test is two-tailed
reject Ho, if to < -2.228 OR if to > 2.228
d.
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.372
since our test is left-tailed
reject Ho, if to < -1.372

level of significance, = 0.05
from standard normal table,right tailed t /2 =1.372
since our test is right-tailed
reject Ho, if to > 1.372

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