1. You have an SRS of size 10 and calculate the one-sample t statistic. What is

Question

1. You have an SRS of size 10 and calculate the one-sample t statistic. What is the critical value such that

(a) t has probability 0.01 to the right of t?

(b) t has probability 0.75 to the left of t?

2.

The one-sample t statistic for testing

H0:=0

Ha:>0

from a sample of n = 15 observations has the value t = 1.82.

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

(b) Give the two critical values t* from Table C that bracket t. What are the one-sided P-values for these two entries?

t*: from to

P-value: from to

(c) Is the value t =1.82 significant at the 5% level? Is it significant at the 1% level? (Yes/Y, No/N)

5%:

1%:

Explanation / Answer

Solution:-

1)

(a) t has probability 0.01 to the right of t is 2.821.

p-value = 0.99

D.F = 10 - 1

D.F = 9

tcritical = 2.821

(b) t has probability 0.75 to the left of t is 0.703.

p-value = 0.75

D.F = 10 - 1

D.F = 9

tcritical = 0.703

2)

The one-sample t statistic for testing

H0: = 0

Ha: > 0

From a sample of n = 15 observations has the value t = 1.82.

(a) The degrees of freedom for this statistic is 14.

n = 15

D.F = 15 - 1

D.F = 14

(b) Two critical values t* from Table C that bracket (1.82, infinity). The one-sided P-values for 1.82 is 0.05.

(c) No, The value t = 1.82 is significant at the 5% level beacuse t = 1.82 is greater than the critical value 1.761.

No, it is not significant at the 1% level, beacuse t = 1.82 is less than the critical value 2.624.

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