Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:
We want to know whether cye black increases sensitivity an the average.
(a) State hypotheses, Be sure to define the parameter.
(b) Check conditions for carrying out a significance test.
(c) The of the test is . Interpet this value in context.
- Interpret a Type l error and a Type ll error in context, and give the consequences of each.
- Understand the relationsonship between the significance level at a test P(Type li error), and power.
(b)Conditions for carrying out a significance test is satisfied
(c) It means that at an average of athletes differ from the athletes whose eye black does not increase the sensitivity.
Given in the question that
A significance test is performed to test the sensitivity with eye black and without eye black in athletes.
Sample size . we have to State hypotheses, Be sure to define the parameter.
The differences in sensitivity with eye black minus without eye black are shown below:
Let denote the average sensitivity differential between with and without eye black.
The average sensitivity of eye black is the parameter of interest. The test is carried out to see if the average sensitivity of eye black has increased.
we have to Check conditions for carrying out a significance test.
The following are the requirements for conducting a paired test: 1. A random sample must be chosen.
2. No outliers should exist.
3. The observations are unrelated to one another, or the sample is no more than of the total population.
The students in the sample were chosen at random.
There are no outliers in the data, as seen in the histogram below:
we know that there will be at least students who are athletes.so the condition is also satisfied.
Given in the question that we have to Interpret this value in context.
The value of the test is It means that at an average of athletes differ from the athletes whose eye black does not increase the sensitivity.
Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of adults. Of these, get the flu.
(a) Do these data provide convincing evidence to support the company's claim? Perform an appropriate test to support your answer.
(b) Which kind of mistake - a Type I error or a Type II error-could you have made in (a)? Explain.
(c) From the company's point of view, would a Type I error or Type Il error be more serious? Why?
Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests subjects. Four of these subjects do significantly better than random guessing.
(a) Is it proper to conclude that these four people have ESP? Explain your answer.
(b) What should the researcher now do to test whether any of these four subjects have ESP?
Healthy bones The recommended daily allowance (RDA) of calcium for women between the ages of and years is milligrams (mg). Researchers who were involved in a large-scale study of women’s bone health suspected that their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.
(a) Determine whether there are any outliers. Show your work.
(b) Interpret the P-value in context.
(c) Do these data give convincing evidence to support the researchers’ suspicion? Carry out a test pg to help you answer this question.
Growing tomatoes An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. Researchers randomly selected Variety A and Variety B tomato plants. Then the researchers divide in half each small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The differences give and. A graph of the differences looks roughly symmetric and single-peaked with no outliers. Is there convincing evidence that Variety A has a higher mean yield? Perform a significance test using to answer the question.
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