{"id":161,"date":"2018-03-03T12:56:00","date_gmt":"2018-03-03T11:56:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/03\/hypothesis-testing-problem-question-1in-a-population-the-average-iq\/"},"modified":"2020-11-05T13:45:29","modified_gmt":"2020-11-05T12:45:29","slug":"hypothesis-testing-problem-question-1in-a-population-the-average-iq","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-problem-question-1in-a-population-the-average-iq\/","title":{"rendered":"Hypothesis Testing Problem – Question 1(In a population, the average IQ…"},"content":{"rendered":"
\n
Question<\/b><\/span><\/span>
In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists want to test a new medication to see if it has either a positive or negative effect on intelligence, or not effect at all. A sample of 30 participants who have taken the medication  has a mean of 140. Did the medication affect intelligence?<\/p>\n

Solution Steps<\/span><\/span><\/b>
Follow these simple steps in solving this question. Leave a question at the left of this page if you hava any.<\/p>\n

Step 1: Set up the null and alternate hypothesis<\/b><\/p>\n

H0<\/sub>:<\/b> medication affects intelligence
Ha<\/sub><\/b>: medication does not affect intellignece<\/p>\n

(not that the alternate hypothesis is always the opposite of the null hypothesis)<\/p>\n

Step 2: Determine the type of test to use<\/b>
Since the sample size  is 30, we use the z-test. See why we use the z-test when sample size is 30 and above in Parametric Tests in Statistics, When to use which<\/a><\/p>\n

Step 3: Calculate the tested statistic z using the formula<\/b><\/p>\n

<\/a><\/div>\n
<\/div>\n
<\/div>\n

This formular can also be written like this:<\/p>\n

<\/a><\/div>\n

Using the data given in the equation we would have the following:
\u03bc0<\/sub> = 100
\u03c3 = 15<\/span><\/span>
n = 30<\/span><\/span>
x\u0304n<\/sub> = 140 <\/span><\/span><\/p>\n

Plugging the values into the formular we have:<\/span><\/span><\/p>\n

<\/a><\/div>\n

Step 4:  Look up the values of z ( called the critical value) from statistical tables. <\/b>
You can access statistical table from here. Statistical Table<\/a>
From the table: we get a value of 1.96<\/p>\n

Step 5: Draw a conclusion<\/b>
In this case the tested statistic value of z calculated is more than the critical value obtained from statistical tables.<\/p>\n

14.606 > 1.96 <\/p>\n

 Therefore we reject the null hypothesis.
This means, from the question, that the medication administered does not affect intelligence. <\/p>\n

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