Question

Each observation in a random sample of 101 bicycle accidents resulting in death was classified according to the day of the week on which the accident occurred. Data consistent with information are given in the following table. Based on these data, is it reasonable to conclude that the proportion of accidents is not the same for all days of the week? Use ? = .05. (Use 2 decimal places.)

Day of Week	Frequency
Sunday	13
Monday	12
Tuesday	12
Wednesday	16
Thursday	19
Friday	17
Saturday	12

?² = 1
P-value interval

Answer 1

First we must state our conditions. This is a SRS because it is stated.

Secondly, to figure out normality we must show that the expected values are greater than 5.

We are expecting all the values to be the same on each day(null hypothesis).

We want to prove that perhaps someday of the week has more deaths than other days of the week (alternative hypothesis).

That is,

The day of the week does not matter for number of deaths (independent)

The day of the week does matter for number of deaths (dependent)

Next, we find expected values. With 101 observations and 7 days out of the week we get 14.43 which is greater than 5.

If we put observed values in list 1 and expected values in list 2 we get:

To calculate , Use the following formula:

Here,

O = Observed frequency

E = Expected frequency

= Summation

Then we have a further table:

Gives us a chi squared () value of: 3.45

If we look at chi squared table for with 6 degrees of freedom (number of observations -1).

We see that it is 12.59. Since chi squared, value is less than 12.59 we fail to reject the null

hypothesis.