theme park owner wants to know if the children’s rides are favoring 10 year old girls over 10 year old boys based on height. In other words, does one group taller than the other and thus can go on more rides?
Part a: The owner gathered height data on 10 year old girls and 10 year old boys, see data below. Determine at the 5% significance level if there is evidence that the two genders are not the same height and thus cannot all go on the same rides. Show your work and give your answer 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 doing some research, the owner found the following information about the expected height and standard deviation for 10 year olds. Does that change the result of part a? Show your work and give your answer in complete sentences in context of the problem.
|
10 year old girls |
10 year old boys |
|
|
Average height |
54.5 inches |
54.5 inches |
|
St. deviation |
2.74 inches |
2.71 inches |
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The following table is taken from the results of a longitudinal study of children from a working class community. The study began when these children entered kindergarten and were four or five years old. The information reported below was collected when the respondents were 18.
Using the information from the table below, answer the following questions:
Started fight before the age of 15
|
Boys |
Girls |
Row Total |
|
|
No |
163 |
184 |
347 |
|
(47.0%) |
(53.0%) |
(89.9%) |
|
|
Yes |
32 |
7 |
39 |
|
(82.1%) |
(17.9%) |
(10.1%) |
|
|
Column Total |
195 |
191 |
Grand Total |
|
(50.5%) |
(49.5 %) |
386 |
χ² = 15.9; p <.05
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