1. In the population, the average IQ is 100 with a standard...

1. In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 105. It is assumed that the data are drawn from a normally distributed population with no outliers. Did the medication affect intelligence, using ? = 0.05? (a) State hypotheses appropriate to the research question. (b) Describe what test would you use and state the reasons for your choice. (c) Draw a conclusion in the context of the problem using the p-value. (d) Construct a 95% CI for ?. Conclude in the context of the problem.

Transcript

00:01 Now in this question, you look at iq, right? in the population, the average iq is 100, according to the question, which is a standard deviation of 15.

00:08 And then some scientists want to test a new medication and to see if it has any effects on the intelligence, on the iq, right? so they took a sample of 30 participants, and then they have a mean of 105, right? so you ask to, of course, to test hypothesis, right? so using the at a significant level of 5%.

00:32 So the hypothesis, the non -hypathyst, is what i'm going to test obviously is that the population of the population of the people who took this medication, we have a population of iq mean, i'm going to call mu, equal to 100.

00:53 Okay? and the alternate hypothesis obviously is that a muo not equal to 100, right? so this is two solid tests, two -tab test.

01:03 What test i'm going to use? i'm going to actually use a z test.

01:08 The reason i'm going to use the d test is because i think the sample size is 30, which is big enough for us to use a z test.

01:16 But of course, more accurate you should use the t test.

01:19 But i think in this example, you have 30 plus pence.

01:22 I think it's big enough to use a z test.

01:23 So i'm going to use a z test for this case.

01:28 And they, to do that, of course, you need to calculate the test the statistic.

01:34 And that, of course, is given by the sample me, which is 105 minus the 100, right? the target value and divided by the sample standard deviation, which is 15, divided by the square of the sample size, which actually is 30, right? and if you do this, you found this to be given by actually five times square root of 30 divided by 15, right? and i found this to be actually 1 .83.

02:04 So that's my test statistic.

02:07 And of course, you can also find the p value, right? so the p value is actually, you can find a p by from the from the d table, right? you look up the table correspond to the corresponding to the three -task statistic.

02:23 You will find that the you will find that the p value can be given by.

02:29 So the d table shows, so this score is 1 .83, right? 1 .83, and you look at the tab, you'll find the corresponding value is 3 .36%.

02:41 So 3 .36%...

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