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An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

a).H0:p^=0.5;Ha:p^>0.5

(b) H0:p=0.5;Ha:p>0.5

(c) H0:p=0.5;Ha:p<0.5

(d) H0:p=0.5;Ha:p≠0.5

(e) H0:p>0.5;Ha:p=0.5

Short Answer

Expert verified

The null and alternative hypotheses you would use to test this claim are (b)H0:p=0.5;Ha:p>0.5

Step by step solution

01

Given Information

The hypotheses are statements about the population parameter:

p: population proportion.

μ:population mean.

σ:population standard deviation.

02

Explanation

The null hypothesis states that the population parameter is equal to the value mentioned in the claim:

H0:p=50%=0.50

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

Ha:p>0.50

Therefore, the correct answer is (B).

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Most popular questions from this chapter

A 95%confidence interval for a population mean is calculated to be (1.7,3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" H0:μ=2versus Ha:μ≠2at the A=0.05level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the A=0.05level since this test is connected to the 97.5%confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject H0at level A=0.05.

(e) We would fail to reject H0at level A=0.05.

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.

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using A=0.01 instead of A=0.05.

(c) using A=0.05 instead of A=0.01.

(d) giving the drug to 25 randomly selected students instead of 50.

(e) using a two-sided test instead of a one-sided test.

Significance and sample size A study with 5000 subjects reported a result that was statistically significant at the 5% level. Explain why this result might not be particularly large or important.

Ancient air The composition of the earth’s atmosphere may have changed over time. To try to discover the nature of the atmosphere long ago, we can examine the gas in bubbles inside ancient amber. Amber is tree resin that has hardened and been trapped in rocks. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed. Measurements on 9specimens of amber from the late Cretaceous era (75to95 million years ago) give these percents of nitrogen:

63.465.064.463.354.864.560.849.151.0Explain why we should not carry out a one-sample t test in this setting.

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