Use a= .01 and two-tailed testt= 2.75, df =10. reject, fail to reject t= -5.25, df= 30. reject, fail to reject t= 1.55, df= infinty symbol. reject, fail to reject

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Use a= .01 and two-tailed test

t= 2.75, df =10. reject, fail to reject

t= -5.25, df= 30. reject, fail to reject

t= 1.55, df= infinty symbol. reject, fail to reject

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Step 1

Given α = 0.01 and two tail test.

t = 2.75, degree of freedom = 10

t = -5.25 degree of freedom = 30

t = 1.55 degree of freedom = infinity.

When the degree of freedom is infinite then we say that the distribution is normal distribution and t score is nothing but the Z score. So Z score = 1.55.

For two tail test if test statistic is between tα/2 and t(1-α/2)  critical score then we fail to reject the null hypothesis. If the test statistic is not between tα/2 and t(1-α/2) then we reject the null hypothesis.

Step 2

Given α = 0.01 so α/2 = 0.005 and 1-α/2 = 0.995.

for degree of freedom 10 the value of t critical score tα/2 = t0.05 = 3.169 (you can see it in picture shared the t score correspoding to 10 degree of freedom and α/2 ( area to its right). Since the t distribution is symmetric about 0 we say t0.995 = -3.169 . Here  it is given that the test statistic t score = 2.75. We can see that the test statistic is not between the critical scores -3.169 and 3.169. So we reject the null hypothesis.

for degree of freedom 30 the value of t critical sc...

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