Question

Using Technology. In Exercises 5–8, 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\(\alpha \)= 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

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

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.

Tail of the test

a.

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

Symbolically,\(p < 0.10\).

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

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.

P-value

c.

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

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,\({H_0}:p = 0.10\),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.

Conclusion of the test

e.

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