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Chapter 8: Problem 103

In the mid-1800s, Dr. Ignaz Semmelweiss decided to make doctors wash their hands with a strong disinfectant between patients at a clinic with a death rate of \(9.9 \%\). Semmelweiss wanted to test the hypothesis that the death rate would go down after the new handwashing procedure was used. What null and alternative hypotheses should he have used? Explain, using both words and symbols. Explain the meaning of any symbols you use.

Short Answer

Expert verified
For the Dr. Semmelweis's experiment, the null hypothesis \(H_0\) would be: The death rate is 9.9% even after implementing the new hand-washing procedure (\(H_0: P = 0.099\)). The alternative hypothesis \(H_A\) would be: The death rate is less than 9.9% after implementing the new hand-washing procedure (\(H_A: P < 0.099\) or \(H_1: P < 0.099\)).

Step by step solution

01

Define the Null Hypothesis

The null hypothesis is typically the hypothesis that sample observations result purely from chance. Here we're expecting no change in the death rate after the new hand-washing procedure. So, our null hypothesis \(H_0\) would be: The death rate is 9.9% even after implementing the new hand-washing procedure.
02

Define the Alternative Hypothesis

The alternative hypothesis is what you might believe to be true or hope to prove true. In our case, it would represent a decrease in death rate after the implementation of the new hand-washing procedure: The death rate is less than 9.9% after implementing the new hand-washing procedure. This can be represented as \(H_A\) or \(H_1\).
03

Interpret the Symbols

In these hypotheses, the '9.9%' stands for the death rate in the clinic. The symbols \(H_0\) and \(H_A\) or \(H_1\) are typically used in literature to denote the null and alternative hypothesis respectively. Therefore, \(H_0: P = 0.099\) refers to the null hypothesis that the death rate will remain the same (9.9%), and \(H_A: P < 0.099\) or \(H_1: P < 0.099\) refers to the alternative hypothesis that the death rate will be less than 9.9% after handwashing.

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Most popular questions from this chapter

A researcher studying extrasensory perception (ESP) tests 300 students. Each student is asked to predict the outcome of a large number of coin flips. For each student, a hypothesis test using a \(5 \%\) significance level is performed. If the \(\mathrm{p}\) -value is less than or equal to \(0.05\), the researcher concludes that the student has ESP. Assuming that none of the 300 students actually have ESP, about how many would you expect the researcher to conclude do have ESP? Explain.

Give the null and alternative hypotheses for each test, and state whether a one-proportion z-test or a two-proportion z-test would be appropriate. a. You test a person to see whether he can tell tap water from bottled water. You give him 20 sips selected randomly (half from tap water and half from bottled water) and record the proportion he gets correct to test the hypothesis. b. You test a random sample of students at your college who stand on one foot with their eyes closed and determine who can stand for at least 10 seconds, comparing athletes and nonathletes.

According to a 2017 AAA survey, \(35 \%\) of Americans planned to take a family vacation (a vacation more than 50 miles from home involving two or more immediate family members. Suppose a recent survey of 300 Americans found that 115 planned on taking a family vacation. Carry out the first two steps of a hypothesis test to determine if the proportion of Americans planning a family vacation has changed. Explain how you would fill in the required entries in the figure for # of success, # of observations, and the value in \(\mathrm{H}_{0}\).

Pew Research published survey results from two random samples. Both samples were asked, "Have you listened to an audio book in the last year?" The results are shown in the table below. $$\begin{aligned}&\begin{array}{l}\text { Listened to an audio } \\\\\text { book }\end{array} & \mathbf{2 0 1 5} & \mathbf{2 0 1 8} & \text { Total } \\ &\hline \text { Yes } & 229 & 360 & 589 \\\&\hline \text { No } & 1677 & 1642 & 3319 \\\&\hline \text { Total } & 1906 & 2002 & \\ &\hline\end{aligned}$$ a. Find and compare the sample proportions that had listened to an audio book for these two groups. b. Are a greater proportion listening to audio books in 2018 compared to 2015 ? Test the hypothesis that a greater proportion of people listened to an audio book in 2018 than in \(2015 .\) Use a \(0.05\) significance level.

Refer to Exercise \(8.97 .\) Suppose 14 out of 20 voters in Pennsylvania report having voted for an independent candidate. The null hypothesis is that the population proportion is \(0.50 .\) What value of the test statistic should you report?
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