Question

The one-sample t statistic for testing H0: μ = 40 Ha: μ ≠ 40 from a sample of n = 13 observations has the value t = 2.77.

(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 < 0.01

0.01 < P < 0.02

0.02 < P < 0.04

0.04 < P < 0.05

0.05 < P < 0.1

(d) Is the value t = 2.77 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

Given :-

Ho : μ = 40

$\large H_a : \mu \neq 40$

n= 13,

t = 2.77

a)

Degree of freedom (df) = n-1 = 13-1 =12

b)

At alpha=5% then critical value is, t* = $\large \pm$ 2.179

c)

p-value = 0.0170

0.01 < p < 0.02

d)

Yes, at 5% level is significantly difference.

No, at 1% level is not significantly difference.

e)

At 5% level then p-value = =TDIST(2.77,12,2) = 0.0170