Question

1) The one-sample t statistic for testing

H₀: μ = 10

H_a: μ > 10

from a sample of n = 19 observations has the value t = 1.83.

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

(d) Is the value t = 1.83 significant at the 5% level?

Yes

No    

Is it significant at the 1% level?

Yes

No    
(e) If you have software available, find the exact P-value. (Round your answer to four decimal places.)

2) The one-sample t statistic for testing

H₀: μ = 40

H_a: μ ≠ 40

from a sample of n = 15 observations has the value t = 2.73.

(a)

What are the degrees of freedom for t?

(b)

Locate the two critical values t* from the Table D that bracket t.

< t <

(c)

Between what two values does the P-value of the test fall?

0.005 < P < 0.010.01 < P < 0.02    0.02 < P < 0.040.04 < P < 0.050.05 < P < 0.1

(d)

Is the value t = 2.73 statistically significant at the 5% level?

Yes

No    

Is it significant at the 1% level?

Yes

No    

(e)

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

Answer 1

1.

(a)

Degree of freedom of t test is,=n−1

=19−1

=18

(b)

t ∗ = 1.84 is bracketed by t = 1.734 (with right-tail probability 0.05) and t = 2.1 (with right-tail probability 0.025).

Hence, because this is a one-sided significance test, 0.025 < P-value < 0.05.

(c)

0.025 < P < 0.05

(d)

This test is significant at the 5% level because the P-value < 0.05.

It is not significant at the 1% level because the P-value > 0.01.

(e) The p-value is .0419.

The result is significant at p < .05