Question

HW8#10

A certain drug is used to treat asthma. In a clinical trial of the​ drug,17 of 288 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 10​% 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.

A. Is the test two-tailed, Left-tailed, or right tailed?

B. What is the test statistic?

   z=

   Round two decimal places as needed.

C. What is the P-value?

Round four decimal places as needed.

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

E. What is the final conclusion?

   There is or is not sufficient evidence?

Answer 1

Solution:-

A) Left tailed test.

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

Null hypothesis: P > 0.10
Alternative hypothesis: P < 0.10

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

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

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

S.D = 0.01768
B)

z = (p - P) / S.D

z = - 2.32

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

C)

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 2.32.

Thus, the P-value = 0.01

D) Interpret results. Since the P-value (0.01) is less than the significance level (0.05), we have to reject the null hypothesis.

E) There is sufficient evidence in the favor of the claim that  less than 10​% of treated subjects experienced headaches.