theme park owner wants to know if the children’s rides arefavoring 10 year old girls over 10 year old boys based on height.In other words, does one group taller than the other and thus cango on more rides?
Part a: The ownergathered height data on 10 year old girls and 10 year old boys, seedata below. Determine at the 5% significance level if there isevidence that the two genders are not the same height and thuscannot all go on the same rides. Show your work and give youranswer in complete sentences in context of the problem.
| 10 year old girls | 10 year old boys |
| 52.3 | 58.1 |
| 53.5 | 53.0 |
| 53.6 | 56.2 |
| 53.0 | 54.2 |
| 56.9 | 50.9 |
| 51.2 | 54.4 |
| 48.6 | 51.4 |
| 51.3 | 53.5 |
| 53.9 | 51.0 |
| 54.0 | 59.7 |
| 57.5 | 53.4 |
| 53.7 | 49.2 |
| 55.7 | 55.7 |
| 54.9 | 55.1 |
| 57.9 | 57.7 |
| 56.9 | 57.7 |
| 59.9 | 52.6 |
| 56.6 | 54.7 |
| 54.6 | |
| 52.9 | |
| 52.0 | |
| 56.0 | |
Part b: After doingsome research, the owner found the following information about theexpected height and standard deviation for 10 year olds. Does thatchange the result of part a? Show your work andgive your answer in complete sentences in context of theproblem.
| 10 year old girls | 10 year old boys |
Average height | 54.5 inches | 54.5 inches |
St. deviation | 2.74 inches | 2.71 inches |
