The one-sample t statistic for testing H 0 : = 10 H a : > 10 from a sample of n

Question

The one-sample t statistic for testing

H0: = 10

Ha: > 10

from a sample of n = 25 observations has the value t = 2.42.

(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 = 2.42 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.)

Explanation / Answer

Given:-

The one-sample t statistic for testing

H0: = 10

Ha: > 10

from a sample of n = 25 observations has the value t = 2.42

degree of freedom = n-1 = 25-1 = 24

Given test is one sided right tailed t test

Therefore we can use alpha = 5% = 0.05

Then the critical value is

tc = t0.05,24 = 1.711

P-Value is 0.011729.
The result is significant at p < 0.05.

For alpha = 1% = 0.01

Then critical value is,

tc = t0.01,24 = 2.492

The P-Value is 0.011729.
The result is not significant at p < 0.01

Both p-value are lies between 0.01 < p < 0.02

e) alpha = 5% & 1% p-value = 0.0118

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