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Chapter 8: Q5 (page 383)

Using Technology. In Exercises 5鈥�8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use 伪= 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

Adverse Reactions to Drug The drug Lipitor (atorvastatin) is used to treat high cholesterol. In a clinical trial of Lipitor, 47 of 863 treated subjects experienced headaches (based on data from Pfizer). The accompanying TI@83/84 Plus calculator display shows results from a test of the claim that fewer than 10% of treated subjects experience headaches.

Short Answer

Expert verified

a. The test is left-tailed.

b. The value of the test statistic (z-score) is equal to -4.459.

c. The p-value is equal to 0.00000412.

d. The null hypothesis is that the proportion of treated subjects who experience headaches is equal to 10%.The null hypothesis is rejected.

e. There is enough evidence to conclude that the proportion of treated subjects who experience headaches is less than 10%.

Step by step solution

01

Given information

It is given that out of 863 subjects who were treated with the drug Lipitor, 47 of them experienced headaches. A claim is made that less than 10% of the treated subjects experience headaches.

02

Tail of the test

a.

According to the given claim, the proportion of treated subjects who experience headaches (p) is less than 10%.

Symbolically, p<0.10.

As there is a less than sign in the given claim, the test is left-tailed.

03

Test statistic

b.

The test statistic to test the given claim is the z-score.

Here, the value of the test statistic (z-score) is equal to -4.459.

04

P-value

c.

The p-value corresponding to the z-score of -4.459 is equal to 0.00000412 (in decimals).

05

Null hypothesis and its conclusion

d.

The null hypothesis for this test is as follows:

Null hypothesis: The proportion of treated subjects who experience headaches is equal to 10%.

Symbolically, H0:p=0.10,where

p is the proportion of treated subjects who suffer from headaches.

Here, the p-value equal to 0.00000412 is less than the significance level of 0.05. Thus, the null hypothesis is rejected.

06

Conclusion of the test

e.

There is enough evidence to conclude that the proportion of treated subjects who experience headaches is less than 10%.

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. Should this be comforting to physicians?

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In Exercises 9鈥�12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 5 鈥淥nline Data鈥�

Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Births A random sample of 860 births in New York State included 426 boys. Use a 0.05 significance level to test the claim that 51.2% of newborn babies are boys. Do the results support the belief that 51.2% of newborn babies are boys?

Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

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