Question

In: Statistics and Probability

An experiment was conducted to test the effect of a new drug on a viral infection....

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 0.36 and 0.64, 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.

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 not rejected. There is insufficient evidence to indicate that the drug is effective in treating the viral infection.

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 sufficient 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.

(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 two decimal places.)

_____ to _____

You may need to use the appropriate appendix table or technology to answer this question.

Solutions

Expert Solution

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1> P2
Alternative hypothesis: P1 < P2

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.50

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.10
z = (p1 - p2) / SE

z = - 2.80

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.80.

Thus, the P-value = 0.003

Interpret results. Since the P-value (0.003) is less than the significance level (0.05), we have to reject the null hypothesis.

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

b) 95% confidence interval to estimate the actual difference (p1 ? p2) in the survival rates for the treated versus the control groups is C.I = (-0.476, - 0.084).

C.I = 0.36 - 0.64 + 1.96 × 0.10

C.I = - 0.28 + 0.196

C.I = (-0.476, - 0.084)


Related Solutions

An experiment was conducted to test the effect of a new drug on a viral infection....
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...
An experiment was conducted to test the effect of a new drug on a viral infection....
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, p̂1 and p̂2, in the two groups were found to be 0.36 and 0.64, respectively. (a) Is there sufficient...
An experiment was conducted to test the effect of a new drug on a viral infection....
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 0.32 and 0.60, respectively. (a) Is there sufficient...
An experiment was conducted to test the effect of a new drug on a viral infection....
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, p̂1 and p̂2, in the two groups were found to be 0.38 and 0.62, respectively. (a) Find the test...
An experiment was conducted to test the effect of a new drug on a viral infection....
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, p̂1 and p̂2, in the two groups were found to be 0.4 and 0.60, respectively. Find the test statistic...
A researcher was conducted to test the effect of a new drug on viral infection. The...
A researcher was conducted to test the effect of a new drug on viral infection. The infection was put on a group of mice and the mice was randomly split into two groups, different groups. The first group (control group), received no treatment for the infection. The second group received the drug. After a 30-day period, the number of survivors in the two groups were observed, and the test statistic was calculated to be z  =  1.46. If we wish...
An experiment was conducted to test the effect of different lighting systems and the presence or...
An experiment was conducted to test the effect of different lighting systems and the presence or absence of a watchman on the average number of car burglaries per month at a parking garage. The data are in the following table and also in the file GARAGE, where the variables are named BURGLAR, LIGHTING and WATCHMAN. Lighting Watchman Mean Number of Burglaries poor no 2.80 good no 1.00 poor yes 2.40 good yes 0.75 Using the Lenth procedure, find which effect(s)...
You are testing the effect of a new drug to treat severe viral pneumonia. To do...
You are testing the effect of a new drug to treat severe viral pneumonia. To do this you conduct a randomized controlled trial. You enroll 200 participants in your study; 100 are allocated to the intervention arm (they receive the drug) and 100 receive the current standard of care. 7 of the participants in the intervention arm and 15 of the participants in the standard care arm die of pneumonia. a)Calculate the RR of survival. Round to the nearest hundredth....
Q2. A certain anti-viral drug is used to cure an infection and the recovery time being...
Q2. A certain anti-viral drug is used to cure an infection and the recovery time being normally distributed with a mean of 28.2 months and standard deviation of 4.2 months. 25 patients who were administered this drug were randomly selected. Now, answer the following questions with necessary justification. (Be careful to always first check if conditions are appropriate to answer each question. Otherwise, do not proceed with calculation.) [2+2+2+2+2+3=13 points] (a) Compute the mean and standard deviation of the average...
To test the effectiveness of a new drug (Phasomaxtrin) designed to treat Quarantinitis, researchers conducted a...
To test the effectiveness of a new drug (Phasomaxtrin) designed to treat Quarantinitis, researchers conducted a clinical trial. The subjects were 512 adult American volunteers with advanced Quarantinitis. Half were randomly assigned to take the drug and the other half were randomly assigned to take a placebo. Neither the subjects nor the doctors who evaluated them knew who was in which group. After three years, 32 percent of those who got Phasomaxtrin were no longer afraid to keep staying inside,...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT