Does Design A allow use of one-way ANOVA to compare the lists? Does Design B allow use of one-way ANOVA to compare the lists? Briefly explain your answers.

MATLAB: An Introduction with Applications
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how do you answer question 25.30?

**(b)** What hypotheses does ANOVA test in this setting?

**(c)** We do not have all the data. What would you look for in deciding whether you can safely use ANOVA?

**(d)** What is the relationship between the standard error of the mean (SEM) and the standard deviation for a sample? What are the four sample standard deviations? Do they satisfy our rule of thumb for safe use of ANOVA?

**25.30 Can you hear these words?** To test whether a hearing aid is right for a patient, audiologists play a tape on which words are pronounced at low volume. The patient tries to repeat the words. There are several different lists of words that are supposed to be equally difficult. Are the lists equally difficult when there is background noise? To find out, an experimenter had subjects with normal hearing listen to four lists with a noisy background. The response variable was the percent of the 50 words in a list that the subject repeated correctly. The data set contains 96 responses. Here are two study designs that could produce these data:

**Design A.** The experimenter assigns 96 subjects to 4 groups at random. Each group of 24 subjects listens to one of the lists. All individuals listen and respond separately.

**Design B.** The experimenter has 24 subjects. Each subject listens to all four lists in random order. All individuals listen and respond separately.

Does Design A allow use of one-way ANOVA to compare the lists? Does Design B allow use of one-way ANOVA to compare the lists? Briefly explain your answers.

**25.31 More rain for California?** The changing climate will probably bring more rain to California, but we don’t know whether the additional rain will come during the winter wet season or extend into the long dry season in spring and summer. Kenwyn Sutherland of the University of California at Berkeley and his coworkers made artificial pools of open grassland for three treatments added water equal to 20% of annual rainfall either during January to March (winter) or during April to June (spring), and no added water (control). Here are some of the data, for plant biomass (in grams per square meter) produced by each plot in a single year:

- **Winter:** 267.1514, 187.1312, 291.1431, 176.2879, 144.1575, 169.9737
- **
Transcribed Image Text:**(b)** What hypotheses does ANOVA test in this setting? **(c)** We do not have all the data. What would you look for in deciding whether you can safely use ANOVA? **(d)** What is the relationship between the standard error of the mean (SEM) and the standard deviation for a sample? What are the four sample standard deviations? Do they satisfy our rule of thumb for safe use of ANOVA? **25.30 Can you hear these words?** To test whether a hearing aid is right for a patient, audiologists play a tape on which words are pronounced at low volume. The patient tries to repeat the words. There are several different lists of words that are supposed to be equally difficult. Are the lists equally difficult when there is background noise? To find out, an experimenter had subjects with normal hearing listen to four lists with a noisy background. The response variable was the percent of the 50 words in a list that the subject repeated correctly. The data set contains 96 responses. Here are two study designs that could produce these data: **Design A.** The experimenter assigns 96 subjects to 4 groups at random. Each group of 24 subjects listens to one of the lists. All individuals listen and respond separately. **Design B.** The experimenter has 24 subjects. Each subject listens to all four lists in random order. All individuals listen and respond separately. Does Design A allow use of one-way ANOVA to compare the lists? Does Design B allow use of one-way ANOVA to compare the lists? Briefly explain your answers. **25.31 More rain for California?** The changing climate will probably bring more rain to California, but we don’t know whether the additional rain will come during the winter wet season or extend into the long dry season in spring and summer. Kenwyn Sutherland of the University of California at Berkeley and his coworkers made artificial pools of open grassland for three treatments added water equal to 20% of annual rainfall either during January to March (winter) or during April to June (spring), and no added water (control). Here are some of the data, for plant biomass (in grams per square meter) produced by each plot in a single year: - **Winter:** 267.1514, 187.1312, 291.1431, 176.2879, 144.1575, 169.9737 - **
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