Question

In: Statistics and Probability

Suppose the 86% confidence for μ is (5.619, 8.781) and the 94% confidence for μ is...

Suppose the 86% confidence for μ is (5.619, 8.781) and the 94% confidence for μ is (4.963, 9.437). We will now consider hypotheses tests of H0: μ = μh vs. Ha: μ ≠ μh.

a. Suppose the hypothesized mean μh is 9.164. What is the most specific statement one can make about the P-value?

b. Suppose the hypothesized mean μh is 4.722. What is the most specific statement one can make about the P-value?

c. Suppose the hypothesized mean μh is 7.935. What is the most specific statement one can make about the P-value?

d. Suppose the hypothesized mean μh is 8.781. What is the most specific statement one can make about the P-value?

Expert Solution

(a)

Since 86% confidence interval does not contain 9.164 so we reject the null hypothesis at 100% - 86% = 14% level of significance. That is p-value must be less than 14% or 0.14.

Since 94% confidence interval contains 9.164 so we fail to reject the null hypothesis at 100% - 94% = 6% level of significance. That is p-value must be greater than 6% or 0.06.

That is p-value is between 0.06 < p-value <= 0.14.

(b)

Since 86% confidence interval does not contain 4.722 so we reject the null hypothesis at 100% - 86% = 14% level of significance. That is p-value must be less than 14% or 0.14.

Since 94% confidence interval does not contain 4.722 so we reject the null hypothesis at 100% - 94% = 6% level of significance. That is p-value must be less than 6% or 0.06.

That is p-value is p-value < 0.06.

(c)

Since 86% confidence interval contains 7.935 so we fail to reject the null hypothesis at 100% - 86% = 14% level of significance. That is p-value must be greater than 14% or 0.14.

Since 94% confidence interval contains 7.935 so we fail to reject the null hypothesis at 100% - 94% = 6% level of significance. That is p-value must be greater than 6% or 0.06.

That is p-value is between p-value > 0.14

(d)

Since 86% confidence interval contains 8.781 so we fail to reject the null hypothesis at 100% - 86% = 14% level of significance. That is p-value must be greater than 14% or 0.14.

Since 94% confidence interval contains 8.781 so we fail to reject the null hypothesis at 100% - 94% = 6% level of significance. That is p-value must be greater than 6% or 0.06.

That is p-value is between p-value > 0.14

orchestra answered 1 year ago

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