The health director of a large company is concerned about the effects of stress on the company’s middle-aged male employees. According to the National Center for Health Statistics, the mean systolic blood pressure for males 35 to 44 years of age is 128. The health director examines the medical records of a random sample of 72 male employees in this age group. The Minitab output below displays the results of a significance test and a confidence interval.
1. Do the results of the significance test allow us to conclude that the mean blood pressure for all the company’s middle-aged male employees differs from the national average? Justify your answer.
2. Interpret the 95% confidence interval in context. Explain how the confidence interval leads to the same conclusion as in Question 1.
Part (a) Test is not significant.
Part (b) Null hypothesis is rejected.
The p-value as indicated in the Minitab output is equal to 0.275 which is greater than 0.05. As a result, the test is not significant and there is insufficient evidence to reject the null hypothesis that there is no difference.
The sample mean and test statistic as indicated in the Minitab output is equal to 129.93 and 1.10 respectively. If the sample means is extended to either side of the test statistic at a 95% confidence interval will still belong to the confidence interval. As a result, it shows there is insufficient evidence to reject the null hypothesis that there is no difference.
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.
Filling cola bottles Bottles of a popular cola are supposed to contain milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are
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?
Heat through the glass How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about . The National Institute of Standards and Technology provides exact data on properties of materials. Here are measurements of the heat conductivity of randomly selected pieces of a particular type of glass:
Is there convincing evidence that the conductivity of this type of glass is greater than ? Carry out a test to help you answer this question.
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