Question

In a clinical​ trial, 2222 out of 867867 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 2.12.1​% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.12.1​% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.1α=0.1 level of​ significance? Find the p-value

Answer 1

Answer:

Claim: To check whether the proportion of drug's users experience flulike symptoms as a side effect is more than 2.1% or not.

The Hypothesis is

H0: P = 0.021

H1: P > 0.021

Now,

n = number of patients = 867

x = number of patients taking a prescription drug daily complained of flulike symptoms=22

Now, we estimate the proportion p as

p̂ = x / n = 22 / 867 = 0.025

Test statistic:

= (0.025 – 0.021) / sqrt[0.021 * (1-0.021) / 867]

= 0.82

Now we find the P-value

= level of significance= 0.01

P-Value = P(Z > 0.82) this is right one tailed test

= 1- P( Z < 0.82)

= 0.4122

= 0.4122

Decision:

Here P-value > 0.01

That is here we fail to reject Ho (Null Hypothesis)

Conclusion:

That is there is not sufficient evidence that the proportion of drug's users experience flulike symptoms as a side effect is more than 2.1%