Which of the following statements are true: (i) Increasing sample size while keeping the same confidence level increases the width of the confidence interval and improves the accuracy of your estimate. (ii) The T distribution curve is centered at 0 and symmetric. Furthermore, the T distribution curve has a thicker tail than the standard Normal curve and comes close to the standard Normal curve as the sample size decreases. (iii) The conclusion of a right tail hypothesis test (test of significance) for a population mean at the significance level should always match the conclusion of a two-sided confidence interval for estimating the same population mean at the confidence level 1- (iv) Keeping all other quantities fixed, increasing the significance level will increase the power of the test.

(iii) The conclusion of a right tail hypothesis test (test of significance) for a population mean at the significance level should always match the conclusion of a two-sided confidence interval for estimating the same population mean at the confidence level 1- (iv) Keeping all other quantities fixed, increasing the significance level will increase the power of the test.

Explanation:

Improving your process decreases the standard deviation and, thus, increases power. Use a higher significance level (also called alpha or α). Using a higher significance level increases the probability that you reject the null hypothesis. ... (Rejecting a null hypothesis that is true is called type I error.)

Increase the power of a hypothesis test

1. Use a larger sample. ...

2. Improve your process. ...

3. Use a higher significance level (also called alpha or α). ...

4. Choose a larger value for Differences. ...

5. Use a directional hypothesis (also cathe called a one-tailed hypothesis).

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.