A software design firm has recently developed a prototype educational computer game for children.

One of the important factors in the success of a game like this is the time it takes the child to play the game.

Two factors are important: the mean time it takes to play and the variability in time required from child to child. Experience indicates that the mean time should be 10 minutes or less and the standard deviation should not exceed 4 minutes. The company has decided to test this prototype with 10 children selected at random from the local school district. The following values represent the time (rounded to the nearest minute) each child spent until completing the game:

9 14 11 8 13 15 11 10 7 12

a. The developers of the software will assume the mean time to completion of the game is 10 minutes or less unless the data strongly suggest otherwise.
State the appropriate null and alternative hypotheses for testing the requirement regarding the mean value.

b. Referring to part

a, test the hypotheses using a significance level equal to 0.10. What assumption will be required?

c. The developers of the software will assume the standard deviation of the time to completion of the game does not exceed 4 minutes unless the data strongly suggest otherwise. State the appropriate null and alternative hypotheses regarding the standard deviation. Use the sample data to conduct the hypothesis test with a significance level  0.10.