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Q.98

Expert-verified

The Practice of Statistics for AP

Found in: Page 592

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

What is significance good for? Which of the following questions does a significance test answer? Justify your answer.
(a) Is the sample or experiment properly designed?
(b) Is the observed effect due to chance?
(c) Is the observed effect important?

(a)It cannot check whether the sample or the experiment is properly designed or not.

(b) Yes, the significant tests finds that the observed effect is due to chance.

(c) It cannot tell if the observed effect is important or not.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1 : Given Information

We have to fin out that Is the sample or experiment properly designed.

Part (a) Step 2: Explanation

A significance test tests the claim made. It investigates the claim by forming the null hypothesis and alternate hypothesis. It accepts or rejects the hypothesis on the basis of $p$ - value. It cannot check whether the sample or the experiment is properly designed or not.

Part (b) Step 1: Given Information

We have to find out Is the observed effect due to chance.

Part (b) Step 2: Explanation

Yes, the significance test finds that the observed effect is due to chance. The significance test measures the observed difference between the group using the $p$ -value. The observed effect is due to chance only if the observed effect has a value more than calculated value at the given significance level.

If the $p - v a l u e < α$ , accept the null hypothesis.

If the $p - v a l u e \geq α$ reject null hypothesis.

In the second case, observed effect has a value more than calculated value.

Part (c) Step 1: Given Information

We have to find out that Is the observed effect important.

Part (c) Step 2: Explanation

A significance test tests the claim made. It cannot tell if the observed effect is important or not. It can only test the claim on the basis of $p$ -value and cannot check if the observed effect is important.

Most popular questions for Math Textbooks

After checking that conditions are met, you perform a significance test of $H_{0} : μ = 1$ versus $H_{α} : μ \neq 1$ . You obtain a $P$ value of $0.022$ . Which of the following is true?

(a) A $95 %$ confidence interval for $μ$ will include the value $1$

(b) A $95 %$ confidence interval for $μ$ will include the value $0$ .

(c) A $99 %$ confidence interval for $μ$ will include the value $1$

(d) A $99 %$ confidence interval for $μ$ will include the value $0$

(e) None of these is necessarily true.

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was $7$ years with standard deviation $2$ years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of $7.5$ that was true $20$ years ago? To determine this, we test the hypotheses $H_{0} : μ = 7.5$ versus $H_{a} : μ \neq 7.5$ using a one-sample $t$ test. What conclusion should we draw at the $5 %$ significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still $7.5$ years.

(d) There is convincing evidence that the mean time working with the postal service is now $7$ years.

(e) We cannot draw a conclusion at the $5 %$ significance level. The sample size is too small.

Which of the following 95% confidence intervals would lead us to reject $H 0 : p = 0.30$ in favor of $H a : p \neq 0.30$ at the 5% significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) None of these

(b) (0.19, 0.27) (d) (0.24, 0.30)

Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. The following table displays the data on yield (lb/acre).

(a) How can the Random condition be satisfied in this study?

(b) Perform an appropriate test to help answer the research question. Assume that the Random condition is met. What conclusion would you draw?

Does this paper give convincing evidence that the mean amount of sugar in the hindguts under these conditions is not equal to $7 m g$ ? Justify your answer.

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