Question

After reviewing data from a sample, an inference can be made about the population. For example,

Find a data set on the internet. Some suggested search terms: Free Data Sets, Medical Data Sets, Education Data Sets.

Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two tailed) would you have to complete?

Show work

Answer 1

Here the problem is :

A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15.

To solve the above problem,we proceed as step by step:

Step 1: State the Null hypothesis. The accepted fact is that the population mean is 100, so: H0: μ=100.

Step 2: State the Alternate Hypothesis. The claim is that the students have above average IQ scores, so:
H1: μ > 100.
The fact that we are looking for scores “greater than” a certain point means that this is a one-tailed test.

Step 3: Draw a picture to help you visualize the problem.

Step 4: State the alpha level. If you aren’t given an alpha level, use 5% (0.05).

Step 5: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.

Step 6: Find the test statistic using this formula:
For this set of data: z= (112.5-100) / (15/√30)=4.56.

Step 6: If Step 6 is greater than Step 5, reject the null hypothesis. If it’s less than Step 5, you cannot reject the null hypothesis. In this case, it is greater (4.56 > 1.645), so you can reject the null.