Step 1:

Claim : The Car accidents are equally distributed for each of the 12 months.

Hypothesis test for the claim :

One of these statements must become the null hypothesis , and the other should be the alternate hypothesis.

The car accidents are equally distributed, hence the proportion of car accident for each month is .

Null hypothesis : \ \

The null hypothesis contains equality.

So for the above, the null hypothesis H₀ : p = 0.5. \ \

Alternate hypothesis :

The statement that does not contain equality is the alternative hypothesis.

So for the above scenario, the alternate hypothesis H_a : .

Step 2:

Find Chi square statics.

Chi square statics are calculated by the formula : .

It is expected that number of car accidents are equally likely for 12 months.

Total Observed frequency is 512.

Therefore expected frequency is .

Chi square statics  : .

Step 3:

Step 4:

Find the critical values.

Significance value is 0.05.

.

The sample size is 12.

Degree of freedom .

Calculate the critical values using calculator.

Follow these steps to evaluate critical values.

1.Select invT()

[2nd --> VARS --> 4 ]

2.Enter the values of and df.

area : 0.05

df : 11

3.Now press Enter in calculator to view answer.

invT(0.05, 12)

=-1.79588

Critical value is -1.79588.

Step 5:

Reject H₀ if .

Chi square statics  : .

Critical value is -1.79588.

.

Reject H₀ as .

Conclusion :

There is insufficient evidence to warrant rejection of the claim that the car accidents are equally distributed for each of the 12 months.

Step 6:

A Elizabethtown firefighter said that accidents occur more often in the summer.

Since the claim is reject, there is a possiblity of the claim that accidents occur more often in the summer.

Hence the claim that accidents occur more often in the summer is valid.