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 control group received no treatment for the infection, while the other group received the drug. After a 30-day period, the proportions of survivors, p̂1 and p̂2, 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 α = 0.05. State the null and alternative hypotheses. H0: (p1 − p2) < 0 versus Ha: (p1 − p2) > 0 H0: (p1 − p2) = 0 versus Ha: (p1 − p2) > 0 H0: (p1 − p2) = 0 versus Ha: (p1 − p2) < 0 H0: (p1 − p2) = 0 versus Ha: (p1 − p2) ≠ 0 H0: (p1 − p2) ≠ 0 versus Ha: (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 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. (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 three decimal places.) to

Answer 1

(a)

If the drug is effective then  proportions of survivors p̂2 shoudl be greater than p̂1. So hypotheses are:

H0: (p1 − p2) = 0 versus Ha: (p1 − p2) < 0

(b)

Conclusion:

H0 is rejected. There is sufficient evidence to indicate that the drug is effective in treating the viral infection.

(b)

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