| A 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? (Note: amusement parks determine whether someone can go on a ride based on height.) |
| Part a: The owner gathered height data on 10 year old girls and 10 year old boys, see excel document for data. 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. |
| 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 |
| 10 year old girls | 10 year old boys | | Overall | Ho: (girls - boys) = 0 | | | | | | | | F-Test Two-Sample for Variances |
| 52.3 | 58.1 | | | Ha: (girls - boys) not = 0 |
| 53.5 | 53.0 | | | | | | | | | | | | 10 year old girls | 10 year old boys |
| 53.6 | 56.2 | | alpha = 0.05 | | | | | | | | | Mean | 54.4045454545 | 54.3611111111 |
| 53.0 | 54.2 | | First Test: | check variances | | | | | | | | Variance | 6.8671212121 | 7.9966339869 |
| 56.9 | 50.9 | | | | | | | | | | | Observations | 22 | 18 |
| 51.2 | 54.4 | | | Ho: variances are the same | | | | | | | | df | 21 | 17 |
| 48.6 | 51.4 | | | Ha: variance are different | | | | | | | | F | 0.8587514726 |
| 51.3 | 53.5 | | | pvalue | 0.7318071586 | | | | | | | P(F<=f) one-tail | 0.3659035793 |
| 53.9 | 51.0 | | | pvalue > alpha | | | | | | | | F Critical one-tail | 0.4675360873 |
| 54.0 | 59.7 |
| 57.5 | 53.4 | | | do not reject |
| 53.7 | 49.2 |
| 55.7 | 55.7 | | | Assume variance are the same |
| 54.9 | 55.1 |
| 57.9 | 57.7 |
| 56.9 | 57.7 |
| 59.9 | 52.6 | | Second Test: t-test to check the data hypothesis (girls vs boys) | | | | | | | | | t-Test: Two-Sample Assuming Equal Variances |
| 56.6 | 54.7 |
| 54.6 | | | | pvalue | 0.9601213383 | | | | | | | | 10 year old girls | 10 year old boys |
| 52.9 | | | | pvalue > alpha | | | | | | | | Mean | 54.4045454545 | 54.3611111111 |
| 52.0 | | | | Do not reject the null hypothesis | | | | | | | | Variance | 6.8671212121 | 7.9966339869 |
| 56.0 | | | | | | | | | | | | Observations | 22 | 18 |
| | | | | The data suggests there is no difference in the height between girls and boys. | | | | | | | | Pooled Variance | 7.3724295587 |
| | | | | Therefore they can all go on the same rides. | | | | | | | | Hypothesized Mean Difference | 0 |
| | | | | | | | | | | | | df | 38 |
| | | | | | | | | | | | | t Stat | 0.050332157 |
| | | | | | | | | | | | | P(T<=t) one-tail | 0.4800606691 |
| | | | | | | | | | | | | t Critical one-tail | 1.6859544602 |
| | | | | | | | | | | | | P(T<=t) two-tail | 0.9601213383 |
| | | | | | | | | | | | | t Critical two-tail | 2.0243941639 |
h2ba09
Question3.xlsx
