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Chapter 9: Q. 60 (page 565)

Which of the following 95% confidence intervals would lead us to reject H0:p=0.30in favor of Ha:p≠0.30at 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)

Short Answer

Expert verified

(b) (0.19,0.27)

Step by step solution

01

Given information

95% of confidence interval.

H0:p=0.30andHa:p≠0.30

Significant level 5%

02

Explanation

At the nullhypothesis, we test if the proportion is of 0.3, that is: H0:p=0.3

At the alternativehypothesis, we test if the proportion is not equal to 0.3, that is: localid="1650647066210" H1:p≠0.3

We want to reject H0:p=0.3 in favor of H1:p≠0.3 , hence we need an interval that is entirely not equal to 0.3, which is given byoption b.

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Most popular questions from this chapter

Haemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of haemoglobin per deciliter of blood (g/dl) are anaemic. A public health official in Jordan suspects that Jordanian children are at risk of anaemia. He measures a random sample of 50 children.

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ attitudes toward school and study habits. Scores range from 0to200. The mean score for U.S. college students is about 115. A teacher suspects that

older students have better attitudes toward school. She gives the SSHA to an SRS of 45of the over 1000students at her college who are at least 30years of age. Check the conditions for carrying out a significance test of the teacher’s suspicion.

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:μ=15is 0.03.

(a) Does the 99%confidence interval for μinclude 15? Why or why not?

(b) Does the 95%confidence interval for μinclude 15? Why or why not?

After checking that conditions are met, you perform a significance test of H0:μ=1versus Hα:μ≠1. You obtain a Pvalue of 0.022. Which of the following is true?

(a) A95%confidence interval for μwill include the value 1

(b) A 95%confidence interval forμwill include the value 0.

(c) A99% confidence interval forμwill include the value 1

(d) A 99%confidence interval for μwill include the value 0

(e) None of these is necessarily true.

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is μ=11.5. The hardness data for a random sample of 20tablets are

11.62711.61311.49311.60211.36011.37411.59211.45811.55211.46311.38311.71511.48511.50911.42911.47711.57011.62311.47211.531

Is there significant evidence at the5% level that the mean hardness of the tablets differs from the target value? Carry out an appropriate support your answer.
See all solutions

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