The one-sample t statistic for testing H0: = 20 Ha: < 20 based on n = 19 observa

Question

The one-sample t statistic for testing H0: = 20 Ha: < 20 based on n = 19 observations has the value t = 2.51.

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

(b) Between what two values does the P-value of the test fall? (You may use the t distribution critical values table.)

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

(c) If you have software available, find the exact P-value. (Round your answer to four decimal places.)

Explanation / Answer

Solution: Given:

Null hypothesis H0: = 20 and alternative hypothesis Ha: < 20

Sample size = n = 19

t = -2.52

(a) We know degrees of freedom for t test is n - 1.

DF = n-1 = 19-1 = 18

(b) we are gievn alternative hypothesis is left tail, and t = -2.51 and DF = 18

So p value must lies : 0.01 < P < 0.02

(c) Using excel we can find left tail p-value.

Excel command: =TDIST(2.51,18,1)

p-value = 0.0109

Done

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