Question

The one-sample t statistic from a sample of n = 13 observations for the two-sided test of the following hypotheses has the value t 1.49. Hoi 64 H 64 (a) What are the degrees of freedom for t? df = (b) Locate the two critical values t from Table C that bracket t. (Use 3 decimal places.) <t What are the twwo-sided P-values for these two entries? <P-value 1.49 significant at the 10 % level? (d) Is the value t Yes O No Is it significant at the 5% level? O Yes O No

Answer 1

(a) The degrees of freedom fort is n-1 = 13 - 1 = 12. (b) At 10% level of significance and for 12 degrees of freedom, the two critical values are -1.782<*<1.782. (c) The two-sided P-values for these two entries are 0.0375<*<0.9624. These are obtained using the standard normal table. (d) The t-statistic value, t = 1.49 lies between the two critical values. So, the null hypothesis is failed to be rejected. So, the value t= 1.49 is not significant at the 10% level. The p-value is obtained as 0.1620 using the standard normal table which is more than the 5% level of significance indicating that the results is not statistically significant. The level of significance is 0.10 and the power of the test is 0.95. P(Type I error) = 0.10 P(Type II error) = 1 - Power = 1 -0.95 = 0.05