Question

1. Another doctor from Facebook claims that the medication Remdesivir can reduce the time it takes to recover from COVID-19. He states that of the 300 people who got it, 80% of the patients were “recovered” by 8 days. Of the 300 people who didn’t get it, 60% of the patients were recovered by 8 days. So, since you know that doctors are not very good with statistics, you decide to test his data and see if it is effective.   

1. What is the Z-score for this test?

2. What is the P-value for this test?

3. What is the 99% confidence interval for the differences between the groups?  

4. Does this “doctor” have a point?

Another medication, Dexamethasone, was tested and they found the severity of COVID 19 was 40% of lethal. Those that did not take it had a severity of 70% of lethal. This experiment was on a much smaller scale and each group only had 150 people each. See if there is a significant difference in the severity of  symptoms between those taking Dexamethasone and those that don’t.

5. What is the Z-score for this “new” test?

6. What is the P-value for this “new” test?

7. What is the 99% confidence interval for this test?

8. Does this medication seem to have an effect? If so, what type?

Answer 1

A

The appropriate hypotheses for the claim is

H₀: P₁ = P₂ i.e., proportion of patients recovered by 8 days due to the medication Remdesivir is same as proportion of patients recovered by 8 days without the medication.

H₁: P₁ > P₂ i.e._, proportion of patients recovered by 8 days due to the medication Remdesivir is greater than the proportion of patients recovered by 8 days without the medication.

p1 = sample proportion of patients recovered by 8 days due to the medication Remdesivir = 0.80

p2 = sample proportion of patients recovered by 8 days without the medication Remdesivir = 0.60

(1)

The Z-score is

Where

The Z-score is 5.345.

(2)

The p-value is 0.00001.

(3)

The 99% confidence interval for the differences between the groups is given by

(4) Since the p-value is less than the level of significance 0.05, we reject the null hypothesis. So the proportion of patients recovered by 8 days due to the medication Remdesivir is greater than the proportion of patients recovered by 8 days without the medication.

B

The appropriate hypotheses for the claim is

H₀: P₁ = P₂ i.e., there is no significant difference between those groups taking Dexamthasone

H₁: P₁ > P₂ i.e. there is a significant difference between those groups taking Dexamthasone

p1 = sample proportion of patients found to be severe of COVID 19 lethal due to the medication Dexamethasone= 0.40

p2 = sample proportion of patients found to be severe of COVID 19 lethal due to the medication Dexamethasone= 0.70

(1)

The Z-score is

Where

The Z-score is -5.222.

(2)

The p-value is 0.00001.

(3)

The 99% confidence interval for the differences between the groups is given by

(4) Since the p-value is less than the level of significance 0.05, we reject the null hypothesis. So there is a significant difference between the groups taking Dexamthasone and not taking Dexamethasone.

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