1. What effect does changing the significance level α from 0.05 to 0.01 have on…
The probability of a false positive
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It will lower
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The probability of a false negative
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increase
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The sensitivity of a test
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The specificity of a test
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2. What effect does increasing the sample size have on…
The probability of a false positive
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The probability of a false negative
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The sensitivity of a test
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The specificity of a test
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The significance level α
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3. State an appropriate null and alternative hypothesis for each of the following. Also state whether you would use a two-tailed or one tailed test. You have some latitude, but phrase your hypothesis precisely and scientifically (no colloquialisms, etc.).
A test of whether cigarette smoking an increase in the number of lung cancer cases
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An experiment to test whether mean herbivore damage to a genetically modified crop of plants differs from an unmodified crop
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A test of whether industrial effluents from a factory into the Mississippi river are affecting fish density downstream
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A test whether providing municipal safe-injection sites for drug addicts reduces the rate of HIV infection
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A test of how tourist presence affects species density in a national park
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4. In an experiment, female guppies from a wild population are presented with a choice of two males. One of the males is from her own population, whereas the other is from a second population in a nearby stream. The goal of the study is to test whether females have a preference. A total of 20 females is tested, all randomly sampled from the population. Males are also randomly sampled. The same males are never used more than once, to ensure independence of experimental trials. Fourteen females choose the male from their own population, whereas six females choose the male from the other population. Use α=0.05.
What is the null hypothesis?
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What is the alternative hypothesis?
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Is this a one-tailed or two-tailed test? Explain
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What is your test statistic?
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What kind of null distribution would you use to calculate the p-value?
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What is your p-value? Show your work (R code).
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Do you reject the null hypothesis?
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What is the 95% confidence interval? Does it include the result of the study? Interpret the result.
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5. In 1955 John Wayne played Genghis Khan in a movie called
The Conqueror. The movie was not an artistic success. Even more unfortunately, the movie was filmed downwind of the site of 11 previous aboveground nuclear bomb tests. Of the 220 people who worked on the movie, 91 were diagnosed with cancer by the 1970s, including Wayne, his co-stars, and the director. According to large scale epidemiological data, about 14% of the American population in that age group were stricken with cancer within this time frame. We want to know if there is evidence for increased cancer risk for people associated with this film. Use α=0.01.
What is the null hypothesis?
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What is the alternative hypothesis?
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Is this a one-tailed or two-tailed test? Explain
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What kind of null distribution would you use to calculate the p-value?
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What is your test statistic?
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What is your p-value? Show your work (R code).
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Do you reject the null hypothesis?
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What is the 95% confidence interval? Does it include the result of the study? Interpret the result.
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