A new antiviral drug for hepatitis C was administered to 180 randomly chosen pat

Question

A new antiviral drug for hepatitis C was administered to 180 randomly chosen patients who had been diagnosed with this disease. Doctors wanted to know whether a patient's probability of improving was independent of the dose of the drug. They tested

H0:The probability of improving is independent of the dose{"version":"1.1","math":"H_0: ext{The probability of improving is independent of the dose}"}

against

Ha:The probability of improving is not independent of the dose{"version":"1.1","math":"H_a: ext{The probability of improving is not independent of the dose}"}.

Their significance level was =0.05{"version":"1.1","math":"lpha = 0.05"}.

Forty-five (45) of the patients were randomly assigned to each of these treatments: placebo, low dose, medium dose, and high dose. The patients were monitored for 18 weeks, after which doctors screened them to see whether they had improved or not. The results are given in this table:

Explanation / Answer

The observed frequencies are

The Expected frequencies are

The contribution of chisquare values are

Degrees of freedom: 3

Test Statistic, X^2: 13.0000
Critical X^2: 7.814736
P-Value:   0.0046

Here P-value 0.0046 which is less than alpha 005, we reject H0

Thus, we conclude that the probability of improving is not independent of the dose

Placebo Low dose Medium dose High dose Total Improved 7 14 16 23 60 not improve 38 31 29 22 120 Total 45 45 45 45 180

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