Arandom sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. the results are listed below. the age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. calculate the chi-square test statistic used to test the claim that all ages have crash rates proportional to their driving rates.

age > 26 26-45 46-65 45<

drivers 66 39 25 30

a).95.431
b).101.324
c).85.123
d).75.101

D).75.101

Step-by-step explanation:

Previous concepts

The Chi-Square test of independence is used "to determine if there is a significant relationship between two nominal (categorical) variables". And is defined with the following statistic:

Where O represent the observed values and E the expected values.  

State the null and alternative hypothesis

Null hypothesis: All ages have crash rates proportional to their driving rates

Alternative hypothesis: Not All ages have crash rates proportional to their driving rates

The observed values are given by the table given:

Age      <26    26-45       46-65        >45

Drivers   66       39            25             30

Calculate the expected values

In order to calculate the expected values we can use the rates given by the problem:

The age distribution of drivers for the given categories is :

18% for the under 26 group, E1 = 160*0.18=28.8

39% for the 26-45 group, E2=160*0.39=62.4

31% for the 45-65 group, E3=160*0.31=49.6

12% for the group over 65. E4=160*0.12=19.2

Calculate the statistic

Calculate the critical value

First we need to calculate the degrees of freedom given by:

, where k represent the total number of categories, for tis case k=4

We can use a confidence level for example 95%, and the significance would be and we can find the critical value with the following excel code: "=CHISQ.INV(0.95,3)", and our critical value would be

We can calculate also the p value:

And we got the same decision reject the null hypothesis at 5% of significance.

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

6x = 48

i hope this . 6 cards each and a total of $48. dvide each side by 6 and you will have your answer.