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Chapter 9: Q.30 (page 548)

A researcher plans to conduct a significance test at the α=0.01significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type Il error for the particular alternative value of the parameter at which she computed the power is

(a) 0.01

(b) 0.10

(c) 0.89

(d) 0.90

(c) 0.99

Short Answer

Expert verified

The probability that the researcher will commit a Type Il error for the particular alternative value of the parameter at which she computed the power is option b.0.10

Step by step solution

01

Introduction

A type I error is a sort of issue that happens during the speculation testing process when an invalid theory is dismissed, despite the fact that it is precise and ought not to be dismissed.

02

Explanation

Given,

A researcher plans to conduct a significance test at the α=0.01significance level.

power = 0.90

Probabilty of type II error = 1-power

=1-0.90=0.10

Hence option b. 0.10is correct

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Most popular questions from this chapter

In a test of H0:p=0.4against Ha:p≠0.4, a random sample of size 100yields a test statistic of z=1.28. The P-value of the test is approximately equal to

(a) 0.90.

(b) 0.40.

(c) 0.05.

(d) 0.20.

(e) 0.10.

Refer to Exercise 1. In Simon’s SRS, 16 of the students were left-handed. A significance test yields a P-value of 0.2184.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.

Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, a reader posed this question: "Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I'll get at least one apple?" Suppose that the wheels spin independently and that the fre symbols are equally likely to appear on each wheel in a given spin.

(a) Find the probability that the slot player gets at least one apple in one pull of the lever. Show your method clearly.

(b) Now answer the reader's question. Show your method clearly.

Bottles of a popular cola are supposed to contain 300milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are 299.4297.7301.0298.9300.2297.0Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of 300ml? Carry out an appropriate test to support your answer

One-sided test Suppose you carry out a significance test of H0:μ=5versus Ha:μ>5based on a sample of size n=20and obtain t=1.81.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

(b) Redo part (a) using an alternative hypothesis ofHa:μ≠5.
See all solutions

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