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Chapter 9: Q 48. (page 582)

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000registered voters, 482favor the proposition. Explain why it isn’t necessary to carry out a significance test in this setting.

Short Answer

Expert verified

Sample proportion is less than0.5

Step by step solution

01

Given Information

It is given that n=1000

x=482

Claim is greater than50%

02

Explanation and Calculation

As per given data:

Null Hypothesis: H0:p=50%=0.5

Alternative Hypothesis: H1:p>0.5

Sample proportion is calculated as:

p^=xn=4821000=0.485

Claim is population proportion less than 0.5. Sample proportion after calculation is less than 0.5.

So, there is no proof given by sample proportion that alternative hypothesis could be true.

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Most popular questions from this chapter

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of α=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

Packaging DVDs (6.2,5.3) A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier, the diameters of the plastic cases vary Normally with mean μ=5.3inches and standard deviation σ=0.01inch. The DVD manufacturer produces DVDs with mean diameterμ=5.26inches. Their diameters follow a Normal distribution with σ=0.02inch.

a. Let X = the diameter of a randomly selected case and Y = the diameter of a randomly selected DVD. Describe the shape, center, and variability of the distribution of the random variable X−Y. What is the importance of this random variable to the DVD manufacturer?

b. Calculate the probability that a randomly selected DVD will fit inside a randomly selected case.

c. The production process runs in batches of 100 DVDs. If each of these DVDs is paired with a randomly chosen plastic case, find the probability that all the DVDs fit in their cases.

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness μ of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a loud noise as stimulus. The appropriate hypotheses for the significance test are

a. H0:μ=18;Ha:μ≠18

b. H0:μ=18;Ha:μ>18

c. H0:μ<18;Ha:μ=18

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Is there convincing evidence at the 5%level that the mean hardness of the tablets in this batch differs from the target value?
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