Question

We adopt α=.05 and test the hypothesis Ho: μx=50. What conclusion should we draw if... (a) n=10, tcalc = +2.10, and Ha: μx ≠ 50? (b) n=20, tcalc = +2.10, and Ha: μx ≠ 50? (c) n=10, tcalc = +2.10, and Ha: μx > 50? Show the critical value of t for each part.

Answer 1

(A) given that sample size n = 10

degree of freedom = n-1

= 10-1

= 9

using excel function T.INV.2T(alpha,df)

setting alpha = 0.05 and df= 9

t critical = T.INV.2T(0.05,9) = -2.262 and +2.262

t statistic is between the t critical values. So, result is insignificant and we failed to reject the null hypothesis

(B) given that sample size n = 20

degree of freedom = n-1

= 20-1

= 19

using excel function T.INV.2T(alpha,df)

setting alpha = 0.05 and df= 19

t critical = T.INV.2T(0.05,19) = -2.093 and +2.093

t statistic is outside the t critical values. So, result is significant and we can reject the null hypothesis

(C) given that sample size n = 10

degree of freedom = n-1

= 10-1

= 9

using excel function T.INV(alpha,df)

setting alpha = 0.05 and df= 9

t critical = T.INV(0.05,9) = 1.833

t statistic is greater than t critical value. So, result is significant and we can reject the null hypothesis