Question

An experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug. After a 30-day period, the proportions of survivors, p?₁ and p?₂, in the two groups were found to be 0.38 and 0.66, respectively.

(a) Is there sufficient evidence to indicate that the drug is effective in treating the viral infection? Use ? = 0.05.

State the null and alternative hypotheses.

H₀: (p₁ ? p₂) = 0 versus H_a: (p₁ ? p₂) < 0H₀: (p₁ ? p₂) = 0 versus H_a: (p₁ ? p₂) ? 0    H₀: (p₁ ? p₂) < 0 versus H_a: (p₁ ? p₂) > 0H₀: (p₁ ? p₂) = 0 versus H_a: (p₁ ? p₂) > 0H₀: (p₁ ? p₂) ? 0 versus H_a: (p₁ ? p₂) = 0

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statistic	z =
rejection region	z >
	z <

State your conclusion.

H₀ is not rejected. There is sufficient evidence to indicate that the drug is effective in treating the viral infection.H₀ is not rejected. There is insufficient evidence to indicate that the drug is effective in treating the viral infection.    H₀ is rejected. There is sufficient evidence to indicate that the drug is effective in treating the viral infection.H₀ is rejected. There is insufficient evidence to indicate that the drug is effective in treating the viral infection.

(b) Use a 95% confidence interval to estimate the actual difference (p₁ ? p₂) in the survival rates for the treated versus the control groups. (Round your answers to two decimal places.)
to

Answer 1

Soln,

According to question,

given that

also,

a) The hypotheses are

H_o : p₁-p₂=0

H_{a :} p₁-p_2<0

Also given that

Formula used to calculate and n₁=50 and n₂= 50

So Z test two tail test applied hence

Z calculated as, test statistic, Z = -2.802

Hence rejection region   Z< -1.644.

Hence from the above calculation,

Conclusion :

Reject Ho There is sufficient evidence to indicate that the drug is effective in treating the viral infection.

b) at 95 % Confidence interval; computed as

(0.0842 to 0.4476)