Question

1. [12 marks] When treated with a standard hypertension drug, half of patients experience a marked decrease in blood pressure, a quarter of them have a moderate decrease in blood pressure, 10% have only a slight decrease, and the rest have either no change or a slight increase in blood pressure.

When a new drug was trialled on a random sample of 200 hypertension patients, the following results were obtained:

Response: Marked Decrease, Moderate Decrease, Slight Decrease, No change or slight increase

Count: 118 58   14 10

Do these results indicate that outcomes under the new drug differ from those on the standard treatment? Evaluate with a suitable hypothesis test at 1% significance level. If you think the outcomes differ, indicate, with reasons, whether the new drug is better or worse than the standard drug.

answer: To answer this question i found out p-value and X^2 using R studio:

I just want an expert answer as to tell me what could be a better conclusion for this question. And  evaluate with a suitable hypothesis test at 1% significance level.

Categories	Xsq$observed	Xsq$expected	Xsq$residuals
Marked Decrease	118	5o	9.616652
Moderate Decrease	58	50	1.131371
Slight Decrease	14	50	-5.091169
No change or slight increase	10	50	-5.656854
Total	200

Chi-squared test for given probabilities:

X-squared	151.68
Df	3
p-value	< 2.2e-16

From R, X² = 151.68 whilst the P-value = 2.2e-16 which is smaller than 0.01.Hence, we will reject our null hypothesis and concludes that Effect of new drug is not equal to what is being claim.

Answer 1

Null hypothesis: Marked decrease, Moderate decrease, Slight decrease and No Change responses are in the 50:25:10:15 ratio.

Alternative hypothesis: The ratio is different from 50:25:10:15

We use Pearson test statistic for goodness-of-fit.

Chi-Square Goodness-of-Fit Test

Test            Expected    Contribution

Category     Observed    proportion      Counts      to Chi-Sq

1 118 0.50 100        3.2400

2 58 0.25 50        1.2800

3 14 0.10 20        1.8000

4 10 0.15 30       13.3333

We get observed chi-square as 19.6533 with 3 DF and p value almost zero.

Hence we reject the null at 1% level and the effect of new drug is significantly different from that of the standard drug.

To justify whether the new drug is better, we consider the following plot.

We find that the expected frequencies for the first two categories are lower, almost similar for the third category. Therefore, an improvement for the new drug is observed.

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