Question

The one-sample t statistic for testing H0: μ = 10 Ha: μ > 10 from a sample of n = 15 observations has the value t = 1.96. (a) What are the degrees of freedom for this statistic? (b) Give the two critical values t* from the t distribution critical values table that bracket t. < t < (c) Between what two values does the P-value of the test fall? 0.005 < P < 0.01 0.01 < P < 0.02 0.02 < P < 0.025 0.025 < P < 0.05 0.05 < P < 0.1 (d) Is the value t = 1.96 significant at the 5% level? Yes No Correct: Your answer is correct. Is it significant at the 1% level? Yes No Correct: Your answer is correct. (e) If you have software available, find the exact P-value. (Round your answer to four decimal places.)

Answer 1

a) For the given no of sample the degree of freedom=n-1

=15-1

=14

b) The critical value at 0.05 level.of significance is computed using t table shown below as

=1.76

c) The p value will be well within

0.025<p value<0.05.

d) Since the P value is less than level of significance 0.05 hence we can reject the null hypothesis and conclude that the value of T is significant at 0.05.

e) Using software the P - value is calculated as

=0.0351

The T table