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Chapter 9: Q.10 (page 546)
In planning a study of the birth weights of babies whose mothers did not see a
doctor before delivery, a researcher states the hypotheses as
The problem is incorrect as the population mean value is as per the null hypothesis and is less than as per the alternative hypothesis.
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Power A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. To test this claim, a significance test is carried out of
You learn that the power of this test at the 5 % significance level against the alternative p=0.08 is 0.64.
(a) Explain in simple language what "power =0.64" means in this setting.
(b) You could get higher power against the same alternative with the same by changing the number of measurements you make. Should you make more measurements or fewer to increase power? Explain.
(c) If you decide to use in place of , with no other changes in the test, will the power increase or decrease? Justify your answer.
(d) If you shift your interest to the alternative p= 0.07 with no other changes, will the power increase or decrease? Justify your answer.
Are boys more likely? We hear that newborn babies are more likely to be boys than girls. Is this true? A random sample of 25,468 firstborn children included 13,173 boys. Boys do make up more than half of the sample, but of course, we don't expect a perfect 50-50 split in a random sample.
(a) To what population can the results of this study be generalized: all children or all firstborn children? Justify your answer.
(b) Do these data give convincing evidence that boys are more common than girls in the population? Carry out a significance test to help answer this question.
The recommended daily allowance (RDA) of calcium for women between the ages of 18 and 24 years is 1200 milligrams (mg). Researchers who were involved in a large-scale study of women鈥檚 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 36 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鈥� suspicion? Carry out a test to help your answer
You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there.8
(a) State appropriate null and alternative hypotheses. Be sure to define your parameter.
(b) Describe a Type I and a Type II error, and explain the consequences of each.
(c) If you had to choose one of the 鈥渟tandard鈥� significance levels for your significance test, would you choose =0.01, 0.05, or 0.10? Justify your choice.
You are thinking of conducting a one-sample t-test about a population mean M using a significance level. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct?
(a) You should not carry out the test because the population does not have a Normal distribution.
(b) You can safely carry out the test if your sample size is large and there are no outliers.
(c) You can safely carry out the test if there are no outliers, regardless of the sample size.
(d) You can carry out the test only if the population standard deviation is known.
(e) The procedures are robust鈥攜ou can u
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