Question

In a clinical​ trial, 28 out of  830 patients taking a prescription drug daily complained of flu like symptoms. Suppose that it is known that

2.8​% of patients taking competing drugs complain of flu like symptoms. Is there sufficient evidence to conclude that more than

2.8​% of this​ drug's users experience flu like symptoms as a side effect at the level of significance of α=0.05? Use any method, however, follow the PHANTOMS acronym

P - Parameter Statement

H - Hypotheses

A - Assumptions & Conditions

N - Name the Test and state the curve you're using

T - Test Statistic - Round your value to TWO decimals and state the command you used to find this value

O - Obtain the P-Value or Critical Value . State the command you are using to find these values

M - Make a Decision about the Null Hypothesis and explain why

S - State Your Conclusion About the Claim

Answer 1

P - Parameter Statement

More than 2.8​% of patients taking competing drugs complain of flu like symptoms.

H - Hypotheses

H0: p = 0.028

H1: p > 0.028

A - Assumptions & Conditions

np(1-p) = 830 * 0.028 * (1 - 0.028) = 22.58928

The sample can be assumed to be a random sample, the value of np(1-p) is 22.58928, which is greater than or equal to 10 and the sample size can be assumed to be less than or equal to 5% of the population size.

N - Name the Test and state the curve you're using

Since np(1-p) > 10, the sample size is large enough to approximate the sampling distribution of proportion as normal distribution and conduct a one sample z test.

T - Test Statistic

Standard error, SE = = 0.005726287

Sample proportion, = 28 / 830 = 0.03373494

Z = ( - p) / SE = (0.03373494 - 0.028) / 0.005726287 = 1.00

O - Obtain the P-Value or Critical Value .

P-value = P(z > 1.00) = 0.1587

M - Make a Decision about the Null Hypothesis Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0.

S - State Your Conclusion About the Claim

We conclude that there is no significant evidence from the data that the true proportion of patients taking competing drugs complain of flu like symptoms is greater than 2.8%