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1b. The p-value for a t test of a null hypothesis against a two sided alternative...

1b. The p-value for a t test of a null hypothesis against a two sided alternative is 0.00010578. The degrees of freedom are 45. Which of the following is correct concerning the possible values for the t statistic?

a. The t statistic could be 2.5 or -2.5

b. The t statistic can only be 2.5

c. The t statistic can only be -2.5

d. We need more information to determine the value of the t statistic.

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Answer #1

Answer to the question:

Option a: The t statistic could be 2.5 or -2.5.

Explanation: The probability value is very less that is 0.00010578. The t value at this level of CI is not mentioned in the table. So, we will consider the probability value of p=0.001. At p=0.001 and DF=45, the t statistic is 3.476. So, the t will be more than 3.476 or less than -3.476. There is a rule of thumb that if the t value is greater than 2.5 or less than -2.5 then the null hypothesis is generally rejected.

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