A certain drug is used to treat asthma. In a clinicall trial of the drug 20 of 2

Question

A certain drug is used to treat asthma. In a clinicall trial of the drug 20 of 278 treated subjects experienced headaches (based on data from the manufacturer) The accompanying calculator display shows results from a test of the claim that less than 11% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (e) below 1-Propliest propc 0.1 2-2.028018553 P-0.0212791773 p-0.0719424460 n- 278 a. Is the test two-tailed, left-tailed, or right-tailed? O Two-tailed test O Left-tailed test O Right tailed test b. What is the test statistic? (Round to two decimal places as needed) c.What is the P-value? P-value Round to four decimal places as needed)

Explanation / Answer

Solution:-

p = 20/278

p = 0.07194

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

d) (D)

Null hypothesis: P > 0.11

Alternative hypothesis: P < 0.11

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

a) Left tailed test

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.0155

z = (p - P) /

b) z = - 2.455

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 2.455. We use the Normal Distribution Calculator to find P(z < - 2.455) = 0.04.

c) Thus, the P-value = 0.0069

Interpret results. Since the P-value (0.0069) is less than the significance level (0.05), we have to reject the null hypothesis.

e) Reject the null hypothesis becuase the p-value is less than or equal to the significance level, alpha.

f) There is sufficient evidence to support the claim that less than 11% of treated subjects experienced headaches.

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