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Question 3 of 8

A test of H0:μ=0H0:μ=0 against Ha:μ≠0Ha:μ≠0 has test statistic z=1.65z=1.65 .

Use Table C to answer the questions.

Is this test statistically significant at the 5%5% level (α=0.05α=0.05 ) ?

Select the correct response.

No, it is not significant because zz is not larger than 1.9601.960 or smaller than −1.960−1.960 .

Yes, it is significant because zz is larger than 1.9601.960 or smaller than −1.960−1.960 .

No, it is not significant because zz is not larger than 1.6451.645 or smaller than −1.645−1.645 .

Yes, it is significant because zz is larger than 1.6451.645 or smaller than −1.645−1.645 .

Is it statistically significant at the 1%1% level (α=0.01α=0.01 ) ?

Select the correct response.

No, it is not significant because |z||z| is smaller than 2.5762.576 .

Yes, it is significant because |z||z| is smaller than 2.5762.576 .

No, it is not significant because |z||z| is not smaller than 2.3262.326 .

Yes, it is significant because |z||z| is not smaller than 2.3262.326 .

Answer 1

H0:μ=0

Ha:μ≠0

test statistic z=1.65 , α=0.05

Test is significant if we reject the null hypothesis.

Find critical value for two tailed test with 0.05 significance level we get

Critical values = -1.96 , 1.96

Rule to take decision is reject Ho if test statistics lies in rejection region

( test statistics z = 1.65) > ( critical value = -1.96) and ( test statistics= 1.65) < ( critical value= 1.96)

Hence test statistics do not lie in rejection region.

Hence test is not significant.

Answer= No, it is not significant because zz is not larger than 1.960 or smaller than −1.960

2) if =0.01

Similarly, explained above,

Critical values are = -2.576 , 2.576

Here test statistics do not lies in rejecton region

Hence it is not statistically significant.

Answer= No, it is not significant because |z| is smaller than 2.576