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 0.32 and 0.60, 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 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 not 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

Given data

Total number of population (N)=100

No of mices in the first sample(n1)=50

No of mices in the second sample(n2)=50

Propertion of surviver in the group which was not treated

no of surviver for first group X1=50*0.32=16

Propertion of surviver in the group which was treated

no of sample for second group X2=50*0.60=30

a) Now we have to chek the claim that the drug is effective in the treatment that mean claim is

hence

so the hypothesis will be

Now for the test statistic

Since it is a lower tail test so the Z criticle value for the is

so the rejection region is

Z < -1.645

Since Z= -2.80 < = -1.645 so We can say that we have enough evidance to reject the null hypothesis

Conclusion:-

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

b)Now Confidence level=95%

so

Confidence interval will be

CI=

where S standard daviation

now

lower tailed value of

So the lower limit = -0.467

upper limit = -0.093