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Chapter 7: Q15E (page 398)

FDA certification of new drugs. Pharmaceutical companies spend billions of dollars per year on research and development of new drugs. The pharmaceutical company must subject each new drug to lengthy and involved testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. The FDA鈥檚 policy is that the pharmaceutical company must provide substantial evidence that a new drug is safe prior to receiving FDA approval, so that the FDA can confidently certify the safety of the drug to potential consumers.

a. If the new drug testing were to be placed in a test of hypothesis framework, would the null hypothesis be that the drug is safe or unsafe? The alternative hypothesis?

Short Answer

Expert verified
  1. The null hypothesis would be that the drug is unsafe and the alternative hypothesis would be that the drug is safe.

Step by step solution

01

Testing of hypothesis

A statistical hypothesis test is a tool of making statistical decision using experimental data. The hypothesis is an assumption which is tested to check whether the inference drawn from the sample data stand true for the entire population or not.

02

Specifying the null hypothesis

The null hypothesis would be that the drug is unsafe if the new drug testing were to be placed in a test.

03

Specifying the alternative hypothesis

The alternative hypothesis would be that the drug is safe if the new drug testing were to be placed in a test.

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Most popular questions from this chapter

Salaries of postgraduates. The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research was obtained from the National Adult Literacy Survey of more than 25,000 respondents. The survey revealed that males with a postgraduate degree have a mean salary of \(61,340 (with standard error \(Sx\) = \)2,185), while females with a postgraduate degree have a mean of \(32,227 (with standard error \(Sx\) = \)932).

  1. The article reports that a 95% confidence interval for \[{\bf{\mu }}M\] , the population mean salary of all males with post-graduate degrees, is (\(57,050, \)65,631). Based on this interval, is there evidence to say that \[{\bf{\mu }}M\] differs from \(60,000? Explain.
  2. Use the summary information to test the hypothesis that the true mean salary of males with postgraduate degrees differs from \)60,000. Use \(\alpha \) =.05.
  3. Explain why the inferences in parts a and b agree.
  4. The article reports that a 95% confidence interval for \(\mu F\) , the population mean salary of all females with post-graduate degrees, is (\(30,396, \)34,058). Based on this interval, is there evidence to say that \(\mu F\)differs from \(33,000? Explain.
  5. Use the summary information to test the hypothesis that the true mean salary of females with postgraduate degrees differs from \)33,000. Use \(\alpha \) =.05.
  6. Explain why the inferences in parts d and e agree.

A random sample of 80 observations from a population with a population mean 198 and a population standard deviation of 15 yielded a sample mean of 190.

a. Construct a hypothesis test with the alternative hypothesis that\(\mu < 198\)at a 1% significance level. Interpret your results.

b. Construct a hypothesis test with the alternative hypothesis that

at a 1% significance level. Interpret your results.

c. State the Type I error you might make in parts a and b.

Americans鈥� favorite sport. The Harris Poll (December 2013) conducted an online survey of American adults to determine their favorite sport. Your friend believes professional (National Football League [NFL]) football鈥攚ith revenue of about $13 billion per year鈥攊s the favorite sport for 40% of American adults. Specify the null and alternative hypotheses for testing this belief. Be sure to identify the parameter of interest.

Which of the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test

Trading skills of institutional investors. Refer to The Journal of Finance (April 2011) analysis of trading skills of institutional investors, Exercise 7.36 (p. 410). Recall that the study focused on 鈥渞ound-trip鈥� trades, i.e., trades in which the same stock was both bought and sold in the same quarter. In a random sample of 200 round-trip trades made by institutional investors, the sample standard deviation of the rates of return was 8.82%. One property of a consistent performance of institutional investors is a small variance in the rates of return of round-trip trades, say, a standard deviation of less than 10%.

a. Specify the null and alternative hypotheses for determining whether the population of institutional investors performs consistently.

b. Find the rejection region for the test using伪=.05

c. Interpret the value of in the words of the problem.

d. A Minitab printout of the analysis is shown (next column). Locate the test statistic andp-value on the printout.

e. Give the appropriate conclusion in the words of the problem.

f. What assumptions about the data are required for the inference to be valid?
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