Question

7.20 (p427) The one-sample t statistic for testing H0: μ = 8 Ha: μ > 8 from a sample of n=22 observations has the value t = 2.24

a) What are the degrees of freedom for this statistic?

b) (report to 3 decimal places) Give the two critical values t* from Table D that bracket t: Lower: Upper:

c) (report to 2 decimal places) Between what two values does the P-value of the test fall? Lower:    Upper:

d) Is the value t = 2.24 significant at the 5% level? (yes/no)

What about at the 1% level? (yes/no)

Answer 1

a) DF = 22 - 1 = 21

b) At alpha = 0.05, the critical value is t^* = 1.721

c) P-value = P(T > 2.24)

                 = 1 - P(T < 2.24)

                 = 1 - 0.9820

                 = 0.018

0.01 < P-value < 0.02

d) Since the test statistic value is greater than the critical value(2.24 > 1.721), so t = 2.24 is significant at the 5% significance level.

At alpha = 0.01, the critical value is t^* = 2.518

Since the test statistic value is greater than the critical value(2.24 > 2.518), so t = 2.24 is significant at the 1% significance level.