The one-sample t statistic for testing H 0 : ? = 20 H a : ? < 20 based on n = 15

Question

The one-sample t statistic for testing

H0: ? = 20

Ha: ? < 20

based on n = 15 observations has the value

t = ?2.52.

(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 < 0.010.01 < P < 0.02     0.02 < P < 0.0250.025 < P < 0.050.05 < P < 0.1

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

Explanation / Answer

(a)

The degrees of freedom = n - 1 = 14

(b)

The critical values for a t distribution with 14 degrees of freedom are:

2.62449 for quantile = 0.99

2.26378 for quantile = 0.98

Hence with t statistic value = 2.52,

p value P follows -

0.01 < P < 0.02

(c)

The exact p value using R by:

1 - pt(2.52, 14)

is = 0.01225

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.