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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’s 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

Suppose you are interested in conducting the statistical test of \({H_0}:\mu = 255\) against \({H_a}:\mu > 225\), and you have decided to use the following decision rule: Reject H0 if the sample mean of a random sample of 81 items is more than 270. Assume that the standard deviation of the population is 63.

a. Express the decision rule in terms of z.

b. Find \(\alpha \), the probability of making a Type I error by using this decision rule.

a. List three factors that will increase the power of a test.

b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?

Question:Paying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a Pew Internet & American Life Project Survey (October 2010). In a representative sample of 755 adults who use the Internet, 506 admitted

that they have paid to download music. Let p represent the true proportion of all Internet-using adults who have paid to download music.

a. Compute a point estimate of p.

b. Set up the null and alternative hypotheses for testing whether the true proportion of all Internet-using adults who have paid to download music exceeds.7.

c. Compute the test statistic for part b.

d. Find the rejection region for the test if α = 0.01.

e. Find the p-value for the test.

f. Make the appropriate conclusion using the rejection region.

g. Make the appropriate conclusion using the p-value.

Solder-joint inspections. Current technology uses high-resolution X-rays and lasers to inspect solder-joint defects on printed circuit boards (PCBs) (Global SMT & Packaging, April 2008). A particular manufacturer of laser-based inspection equipment claims that its product can inspect, on average, at least 10 solder joints per second when the joints are spaced .1 inch apart. The equipment was tested by a potential buyer on 48 different PCBs. In each case, the equipment was operated for exactly 1 second. The number of solder joints inspected on each run follows:

The potential buyer wants to know whether the sample data refute the manufacturer’s claim. Specify the null and alternative hypotheses that the buyer should 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 “round-trip” 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 usingα=.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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