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.

*H*_{0}: (*p*_{1} ?
*p*_{2}) = 0 versus *H*_{a}:
(*p*_{1} ? *p*_{2}) <
0*H*_{0}: (*p*_{1} ?
*p*_{2}) = 0 versus *H*_{a}:
(*p*_{1} ? *p*_{2}) ?
0 *H*_{0}:
(*p*_{1} ? *p*_{2}) < 0 versus
*H*_{a}: (*p*_{1} ?
*p*_{2}) > 0*H*_{0}:
(*p*_{1} ? *p*_{2}) = 0 versus
*H*_{a}: (*p*_{1} ?
*p*_{2}) > 0*H*_{0}:
(*p*_{1} ? *p*_{2}) ? 0 versus
*H*_{a}: (*p*_{1} ?
*p*_{2}) = 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.

*H*_{0} is not rejected. There is sufficient
evidence to indicate that the drug is effective in treating the
viral infection.*H*_{0} is not rejected. There is
insufficient evidence to indicate that the drug is effective in
treating the viral
infection. *H*_{0} is
rejected. There is sufficient evidence to indicate that the drug is
effective in treating the viral infection.*H*_{0} 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
(*p*_{1} ? *p*_{2}) 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} : p_{1}-p_{2}=0

H_{a :} p_{1}-p_{2<0}

Also given that

Formula used to calculate and n_{1}=50 and
n_{2}= 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)

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