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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 10: Q. AP3.5 (page 701)

Which of the following will increase the power of a significance test?
a. Increase the Type II error probability.
b. Decrease the sample size.
c. Reject the null hypothesis only if the P-value is less than the significance level.
d. Increase the significance level $α$ .
e. Select a value for the alternative hypothesis closer to the value of the null hypothesis.

Short Answer

Expert verified

The correct option is (d) Increase the significance level $α$

Step by step solution

01

Given Information

We have to determine the theory that increase the power of a significance test.

02

Simplification

Atest'spowercanbeincreasedintwoways:byincreasingthesamplesizeorbyraisingthesignificancelevel.

As a result, increasing the power of a significance test with the help of the sigma's significance level.

Hence, the correct option is (d) Increase the significance level $α$

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Most popular questions from this chapter

Based on the P-value in Exercise 71, which of the following must be true?

a. A $90 %$ confidence interval for μM−μF $\frac{305}{1526} = 0.200 = 20.0 % μ_{M} - μ_{F}$ will contain $0$

b. A $95 %$ confidence interval for μM−μF $\frac{305}{1526} = 0.200 = 20.0 % μ_{M} - μ_{F}$ will contain $0$

c. A $99 %$ confidence interval for μM−μF $\frac{305}{1526} = 0.200 = 20.0 % μ_{M} - μ_{F}$ will contain $0$

d. A $99.9 %$ confidence interval for μM−μF $\frac{305}{1526} = 0.200 = 20.0 % μ_{M} - μ_{F}$ will contain $0$

I want red! Refer to Exercise 1.

a. Find the probability that the proportion of red jelly beans in the Child sample is less than or equal to the proportion of red jelly beans in the Adult sample, assuming that the company’s claim is true.

b. Suppose that the Child and Adult samples contain an equal proportion of red jelly beans. Based on your result in part (a), would this give you reason to doubt the

company’s claim? Explain your reasoning.

Flight times The pilot suspects that the Dubai-to-Doha outbound flight typically takes longer. If so, the difference (Outbound−Return) in flight times will be positive on more days than it is negative. What if either flight is equally likely to take longer? Then we can model the outcome on a randomly selected day with a coin toss. Heads means the Dubai-to-Doha outbound flight lasts longer; tails means the Doha-to-Dubai return flight lasts longer. To imitate a random sample of $12$ days, imagine tossing a fair coin $12$ times.

a. Find the probability of getting $11$ or more heads in $12$ tosses of a fair coin.

b. The outbound flight took longer on $11$ of the $12$ days. Based on your result in part (a), what conclusion would you make about the Emirates pilot’s suspicion?

A certain candy has different wrappers for various holidays. During Holiday $1$ , the candy wrappers are $30 %$ silver, $30 %$ red, and $40 %$ pink. During Holiday $2$ , the wrappers are $50 %$ silver and $50 %$ blue. In separate random samples of $40$ candies on Holiday $1$ and $40$ candies on Holiday $2$ , what are the mean and standard deviation of the total number of silver wrappers?

a. $32, 18.4$

b. $32, 6.06$

c. $32, 4.29$

d. $80, 18.4$

e. $80, 4.29$

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. A coin flip was used to determine which plot in each pair got the regular barley seed and which got the kiln-dried seed. The following table displays the data on barley yield (pound per acre) for each plot.

Do these data provide convincing evidence at the $α = 0.05$ level that drying barley seeds in a kiln increases the yield of barley, on average?

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