# Statistics and Probability Questions With Solutions

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• Published : May 22, 2012

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NAME: SHU ZHAOHUI
ID: 17329164

Q5.
Descriptive Statistics|
| N| Minimum| Maximum| Mean| Std. Deviation| Skewness| | Statistic| Statistic| Statistic| Statistic| Statistic| Statistic| Std. Error| Gasolinescore| 1000| 3.00| 21.00| 14.9090| 4.83654| -.493| .077| Globalscore| 1000| 3.00| 21.00| 17.0490| 3.78774| -1.073| .077| Valid N (listwise)| 1000| | | | | | |

The mean in the gaslinescore and globalscore stand for the average the respondents choose is 14.9090 and 17.0490, the respondents choose is concentrate around 14.9090 and 17.0490. The standard deviation of gasolinescore refer to most of the respondents answer is rang from (14.9090-4.83654) to (14.9090+4.83654), and the standard deviation of globalscore refer to most of the respondents answer is rang from (17.0490-3.78774) to (17.0490+3.78774), and the globalscore’s float is smaller than gasolinescore’s float. The data for Gasolinescore and Globalscore are not the normally distributed. Because the normally distributed situation means the median equal to mean. but in the table of above, the gaslinescore’s median(12) is not equal to the mean(14.9090) and the globalscore’s median(12) also not equal to mean(17.0490), they are all negative skew. So the data of each variable is not a normally distributed. If the two variables were normally distributed, the median should be equal to mean, so the mean is 12, and the standard deviation is 4.83654 for gasolinescore; the standard deviation of globalscore is 3.78774. so the upper limits for gasolinescore is (12+4.83654=16.83654) and the lower limits is (12-4.83654=7.16346), the upper limits for globalscore is (12+3.78774=15.78774) and the lower limits is (12-3.78774=8.21226).

Q6.
Case Processing Summary|
| Cases|
| Valid| Missing| Total|
| N| Percent| N| Percent| N| Percent|
Globscorecat * Gasolinecat| 1000| 100.0%| 0| .0%| 1000| 100.0%| The chart means there are 1000 respondents take part in the test of globscorecat and all respondents answer is valid. The same as gasolinecat

Globscorecat * Gasolinecat Crosstabulation|
Count|
| Gasolinecat| Total|
| 1.00| 2.00| 3.00| 4.00| |
Globscorecat| 1.00| 2| 9| 1| 1| 13|
| 2.00| 17| 177| 59| 13| 266|
| 3.00| 5| 261| 441| 7| 714|
| 4.00| 0| 4| 2| 1| 7|
Total| 24| 451| 503| 22| 1000|
This is a cross tabulation of globscorecat and gasolinecat, it easily can be see that a lot of respondents choose 3.00 for answer in globscorecat and gasolinecat. Chi-Square Tests|
| Value| df| Asymp. Sig. (2-sided)|
Pearson Chi-Square| 161.938a| 9| .000|
Likelihood Ratio| 160.193| 9| .000|
Linear-by-Linear Association| 82.785| 1| .000|
N of Valid Cases| 1000| | |
a. 6 cells (37.5%) have expected count less than 5. The minimum expected count is .15.| The a means that we have not violated the assumption, as all our expected cell sizes are greater than 15. Symmetric Measures|

| Value| Asymp. Std. Errora| Approx. Tb| Approx. Sig.| Interval by Interval| Pearson's R| .288| .035| 9.496| .000c| Ordinal by Ordinal| Spearman Correlation| .306| .032| 10.145| .000c| N of Valid Cases| 1000| | | |

a. Not assuming the null hypothesis.b. Using the asymptotic standard error assuming the null hypothesis.c. Based on normal approximation.| Q7.

Descriptive Statistics|
Gender| N| Minimum| Maximum| Mean| Std. Deviation| Skewness| | Statistic| Statistic| Statistic| Statistic| Statistic| Statistic| Std. Error| Male| Gasolinescore| 505| 3.00| 21.00| 14.9584| 4.72164| -.453| .109| | Globalscore| 505| 4.00| 21.00| 17.0218| 3.66254| -.989| .109| | Valid N (listwise)| 505| | | | | | |

Female| Gasolinescore| 495| 3.00| 21.00| 14.8586| 4.95529| -.526| .110| | Globalscore| 495| 3.00| 21.00| 17.0768| 3.91485| -1.146| .110| | Valid N (listwise)| 495|...