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Question 2new drug cures 9 of 200 patients suffering from type of cancer; for which the historical cure rale is 2%_ Perform test t0 check on the significance of thi...

Question

Question 2new drug cures 9 of 200 patients suffering from type of cancer; for which the historical cure rale is 2%_ Perform test t0 check on the significance of this result; at both 5% and 1% levels of 'significance: Based on your conclusion_ comments on the efficacy of the treatment using this new drug: (15 marks)

Question 2 new drug cures 9 of 200 patients suffering from type of cancer; for which the historical cure rale is 2%_ Perform test t0 check on the significance of this result; at both 5% and 1% levels of 'significance: Based on your conclusion_ comments on the efficacy of the treatment using this new drug: (15 marks)



Answers

Suppose that in clinical trials for treatment of a skin disorder 642 of 2105 patients receiving the current standard treatment were cured of the disorder and 697 of 2115 patients receiving a new proposed treatment were cured of the disorder. (a) Does the new procedure cure a higher percentage of patients at the $\alpha=0.05$ level of significance? (b) Do you think that the difference in success rates is practically significant? What factors might influence your decision?

Now in this question, rats with cancer are divided into two groups. Okay. One group receives five mg of a medication that is thought to fight cancer, and the other one receives 10 mg. So what am I doing? I'm trying to change, make some change in racks body. Right. I'm trying to manipulate I'm trying to influence rats health. So this is nothing but an experiment, Right. What is the difference between an observation study and an experiment In an observational study? I'm just a mere spectator. I'm not trying to influence or manipulate the characteristics of the individuals in my population, individuals or entities or whatever. But in this case, I'm actually performing an experiment. Mhm.

And this problem, we're told of a new drug that is that to skew to cure 80% of the patient that it's administered to. And if we have 25 patients, we have to find the following probabilities. The less know important information. No, that P is equal to 0.8. We know that end is equal to 25. Since we will be using the normal approximation, we will need to find mean understand the deviation so mean I was given by n times okay, just equal to 20. And their standard deviation is given better school brooch of 25 times who times one minus b and then is equal Teoh too. So in part in where we asked to find exactly the probability of a bracket 20 people cured, that's the probability were X is equal to 20. We knew that corresponds to the area beneath the bar of the history. Graham from X equal 19.5 two x equal 20.5 So we need to find a correspondent Z scores with those two X values. The 1st 1 we get doing 19.5 minus did mean you better by the standard deviation. This works out to me. Negative point 25 and second, the school Tony Point by minus tourney or her too looks out of me. Positive point toe. The airport of Probability that we have exactly 20 people cured is the call to the probability that the is list and 0.25 minus the probability that is less than negative. 1 to 5 from the the table and get 0.5987 minus 0.40 13 like look Celtel Final probability of approximately 0.1 974 in Part B. We were asked to find a probability and probably see that all are cured. I'm basically we're finding the probability, but X is equal to 25 and we know that corresponds to the area under the bar of our history. Graham from X equal 24.5 two x equal, 25.5 The corresponding Z scores 24 points Bye minus 20 over to gives approximately 2.7 by well, 2.25 brother on the second Z score with 25.5 minus 20 abetted by two right here, 1.75 So the probability that all are cured, called 25 patients are cured will be equal to the probability that B is less than 2.75 Rennes. The probability that city is less than 2.25 just equal to for more table the table 0.9970 finest 0.9878 which gives a final probability of 0.0 nine to imports. They were finding a probability that no one is cured. So this is essentially seen probability. Nothing equals zero. Okay, so disco response to the area under the bar of our history, Graham from X equals negative. They were appointed by to positive zero point by. And if we find the Z scores this find the 1st 1 who Ah, the Okay, approximate me negative zero point kind minus 20. Or her too. That looks out to be approximately negative. Turn point 25 and see to I was being a gold to positive point by you're going find minus 20 invented by two. That is negative 9.25 Just look in the values Looking at the values of our Z score. These are way outside. Three times the standard deviation away from the mean. No, we can see that those probabilities will be so small. Little most. I could be essentially zero if you want to verify that which I did using microscopic. Still, the probability that X is equal to zero actually looked out to be three point 36 times 10 to the negative 18 which is, for all intents and purposes, essentially zero. Finally, we're trying to find a probability that 12 or fewer of the people administer the drug were cured. So this would correspond to the area of all the bars to the left open, we're X is equal to 12.5. Okay, so we find a correspondence, the score to this, and then we'll be able to kind of probability. So it's a is equal to 12.5 minus 20. I read it by two. And that gay approximately. No, I did it three point 75 So we know that the probability that X is less than or equal to tool is equal to the probability that thing is less than or equal to negative. 3.75 Now again, you can use technology to figure out what the correspondent probability you. So if you have is the table that goes all the way to negative for you can just read that off the graph, and that turns out to be approximately their point. Zero Nero 01

Let us look at this question. Rats with cancer are divided into two groups. One group receives 5 mg of medication, so they are actually performing an experiment. In this case, they are trying to modify the group's right. They are bringing in some change. So this is going to be an experiment. This is an experiment.

This question says rats with cancer develop two groups. One group receives 5 mg off medication. So what is happening? We are giving them a treatment. So this is an experiment. We're trying to modify their characteristics. We're trying to modify the subject. So this is an experiment? Definitely. This is my answer.


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