Question

In: Math

In clinical trials of the allergy medicine Clarinex (5 mg), it was reported that 50 out...

In clinical trials of the allergy medicine Clarinex (5 mg), it was reported that 50 out of 1655 individuals in the Clarinex group and 31 out of 1652 individuals in the placebo group experienced dry mouth as a side effect of their respective treatments. Test the hypothesis that a greater proportion of individuals in the experimental group experienced dry mouth compared to the individuals in the control group at the α=0.01 level of significance.

Null Hypothesis:

Alternate Hypothesis:

P-value:

Conclusion:

Interpretation:

Construct a 95% confidence interval for the difference between the two population proportions Experimental – Control. Explain what it means.

Solutions

Expert Solution

Solution:

Here, we have to use z test for the difference in two population proportions.

Null hypothesis: H0: There is no any significant difference in the proportion of individuals in the experimental group and control group experienced dry mouth.

Alternative hypothesis: Ha: A greater proportion of individuals in the experimental group experienced dry mouth compared to the individuals in the control group.

H0: p1 = p2 versus Ha: p1 > p2

This is an upper tailed or right tailed test.

We are given

Level of significance = α = 0.01

Test statistic for z test for two population proportions is given as below:

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Where,

X1 =50

X2 =31

N1 =1655

N2 =1652

P = (X1+X2)/(N1+N2) = (50 + 31)/(1655+1652) = 0.0245

P1 = X1/N1 = 50/1655 = 0.03021148

P2 = X2/N2 = 31/1652 = 0.018765133

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Z = (0.03021148 – 0.018765133) / sqrt(0.0245*(1 – 0.0245)*((1/1655) + (1/1652)))

Z = 2.1292

P-value = 0.0166

(by using z-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that a greater proportion of individuals in the experimental group experienced dry mouth compared to the individuals in the control group.

Now, we have to find the 95% confidence interval for difference between two population proportions.

Confidence interval for difference between two population proportions:

Confidence interval = (P1 – P2) ± Z*sqrt[(P1*(1 – P1)/N1) + (P2*(1 – P2)/N2)]

Confidence level = 95%

Z = 1.96

(by using z-table)

Confidence interval = (P1 – P2) ± Z*sqrt[(P1*(1 – P1)/N1) + (P2*(1 – P2)/N2)]

Confidence interval = (0.03021148 – 0.018765133) ± 1.96*sqrt(0.0245*(1 – 0.0245)*((1/1655) + (1/1652)))

Confidence interval = 0.011446347 ± 1.96*0.0054

Confidence interval = 0.011446347 ± 0.0105

Lower limit = 0.011446347 - 0.0105 = 0.0009

Upper limit = 0.011446347 + 0.0105 = 0.0220

Confidence interval = (0.0009, 0.0220)

We are 95% confident that the difference between population proportions of all individuals in the experimental group and control group will lies within 0.0009 and 0.0220.


Related Solutions

A manufacture of medicine of allergy claims that his medicine is effective in curing allergy in...
A manufacture of medicine of allergy claims that his medicine is effective in curing allergy in at least 75% of cases. His medicine is applied on 100 patients of allergy and 80 were relieved . Test the manufacture's claim at 5%level of significance . this question is from probability subject please do all step and explain it also. i do not know any thing on this
In clinical trials of the anti-inflammatory drug Inflaminex, adult and adolescent allergy patients were randomly divided...
In clinical trials of the anti-inflammatory drug Inflaminex, adult and adolescent allergy patients were randomly divided into two groups. Some patients received 500mcg of Inflaminex, while some patients received a placebo. Of the 2103 patients who received Inflaminex, 520 reported bloody noses as a side effect. Of the 1671 patients who received the placebo, 368 reported bloody noses as a side effect. Is there significant evidence to conclude that the proportion of Inflaminex users who experienced bloody noses as a...
Side Effects for Migraine Medicine In clinical trials and extended studies of a medication whose purpose...
Side Effects for Migraine Medicine In clinical trials and extended studies of a medication whose purpose is to reduce the pain associated with migraine headaches, 2% of the patients in the study experienced weight gain as a side effect. Suppose a random sample of 600 users of this medication is obtained. Explain why you can use normal approximation to binomial distribution to approximate the probabilities below. Approximate, up to 4 decimal digits, the probability that 20 or fewer users will...
Side Effects for Migraine Medicine In clinical trials and extended studies of a medication whose purpose...
Side Effects for Migraine Medicine In clinical trials and extended studies of a medication whose purpose is to reduce the pain associated with migraine headaches, 2% of the patients in the study experienced weight gain as a side effect. Suppose a random sample of 600 users of this medication is obtained. Explain why you can use normal approximation to binomial distribution to approximate the probabilities below. Approximate, up to 4 decimal digits, the probability that 20 or fewer users will...
Clinical trials involved treating flu patients with Tamiflu, which is a medicine intended to attack the...
Clinical trials involved treating flu patients with Tamiflu, which is a medicine intended to attack the influenza virus and stop it from causing flu symptoms. Among 724 patients treated with Tamiflu, 72 experienced nausea as an adverse reaction. (a) Construct a 95% confidence interval for the (population) proportion of patients treated with Tamiflu that experienced nausea as an adverse reaction.   (b) It is reported that the rate of nausea among patients treated with Tamiflu is greater than 7%. Using the...
In a clinical study of an allergy drug, 108 of the 200 subjects reported experiencing significant...
In a clinical study of an allergy drug, 108 of the 200 subjects reported experiencing significant relief from their symptoms. Using a 1% significance level test the claim that more than half of all those using the drug experience relief.
A database of current clinical. trials is found here:https://clinical trials.gov/.look for examples of clinical trials for...
A database of current clinical. trials is found here:https://clinical trials.gov/.look for examples of clinical trials for Crohn's. Are there any trials using fecal transplant or helming therapy that Amelia might consider? Are there alternative treatments not on the list above that she might add to her table?
WHY ARE CLINICAL TRIALS IMPORTANT TO APPROVAL OF NEW DRUGS? WILL YOU PARTICIPATE IN CLINICAL TRIALS,...
WHY ARE CLINICAL TRIALS IMPORTANT TO APPROVAL OF NEW DRUGS? WILL YOU PARTICIPATE IN CLINICAL TRIALS, IF YES WHY AND IF NO, WHY? WHY IS NUTRITION IMPORTANT TO HIV MANAGEMENT? HOW WOULD YOU ENCOURAGE WOMEN TO PROTECT THEMSELVES AGAINST HIV INFECTION? WOMEN ARE MORE LIKELY TO SEXUALLY INFECT THEIR MALE PARTNERS WITH HIV, WHY? WOMEN ARE MORE LIKELY TO SEXUALLY INFECT THEIR MALE PARTNERS WITH HIV, WHY?
1/ In clinical trials of 3066 patients taking treatment​ A, 790 reported nausea as a side...
1/ In clinical trials of 3066 patients taking treatment​ A, 790 reported nausea as a side effect. In clinical trials of 1013 patients taking treatment​ B, 216 reported nausea as a side effect. Researchers want to know whether the difference in sample proportions is statistically significant. Use the​ "Randomization test for two​ proportions" applet in StatCrunch with a seed of 30102. Obtain exactly 3000 runs of the applet. What is the​ P-value based this​ randomization? ​P-value= (Round to four decimal...
The following data describe a clinical trial of an allergy medication: Allergy Drug Placebo Control Total...
The following data describe a clinical trial of an allergy medication: Allergy Drug Placebo Control Total Improvement 65 42 31 138 No Improvement 55 58 49 162 Total 120 100 80 300 a. What is the probability that a randomly selected person in the study was given either the drug or the placebo? b. What is the probability that a randomly selected person either improved or did not improve? c. What is the probability that a randomly selected person either...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT