Conduct a single sample t-test for the data given below. You hope to compare the age (in months) of when your sample of children first began speaking versus the general population. Your sample of children has been presented with a literature and text rich environment from 3 to 6 months of age and you want to see if your children start speaking earlier than the general population of children.

Use the age (in months) given as your sample data (n=15). Assume that the general population of American children begin speaking at 14 months (mu) and that the population standard deviation is unknown.

Age in months your sample of children began speaking.

8

9

10

15

18

17

12

11

7

8

10

11

8

9

12

(Source: Pagano, R. R. (1998). Understanding statistics in the behavioral sciences (5th ed.). Pacific Grove, CA: Brooks/Cole. p. 299)

Step 1 Calculate by hand the appropriate t statistic and determine if it is statistically significant at the alpha=.05 level. Show all calculations. State all parts of the null hypothesis decision strategy using the following headings to organize your assignment.

1. State null and alternative hypotheses.
2. Set alpha level and draw sample. (Just declare the alpha and assume you have drawn a random sample.)
3. Calculate test statistic.
4. Decision and conclusion.
5. Also calculate the appropriate confidence interval for this example. Show all calculations.

Step 2Second, use SPSS or Excel to conduct the same test. In SPSS, you will need to enter the above data set and save the file. Then, you will need to have SPSS compute the single sample t-test for you by doing the following:

1. Click Analyze
2. Click Compare Means on the drop menu.
3. Click One Sample T Test on the drop menu.
4. Move the variable Age to the right window.
5. In the blank next to Test, make sure you enter 14 (the population mean).
6. Click OK.

(Remember to then save your report/output file once you get it, though I am not requiring you to turn this in).

Answer the following questions :

1. What was the t calculated value from the SPSS output? Was it the same as the value you calculated by hand (within rounding error)?
2. From SPSS, what was the exact probability (p calculated) of getting the t calculated value? Was this less or greater than your alpha level?