Statistics- Chi Sqaure

Question

Month	Car Accident
Jan.	38
Feb.	30
Mar.	46
Apr.	40
May	46
June	49
July	47
Aug.	50
Sept.	50
Oct.	42
Nov.	37
Dec.	37

Above is a list of the number of car accidents in the past year in Elizabethtown.

A person claims that the car accidents are equally likely for each of the 12 months.

A. State the null and alternative hypothesis (correct notation).

B. Find Chi-Square test statistic. Either show work or describe calculator steps.

C. Determine if the claim (above) should be rejected or not using a 0.05 sig. level. Show all work

D. A Elizabethtown firefighter said that accidents occur more often in the summer. Using the results from above, do you agree with the commissioner or not?

 

Answer 1

Step 1:

(A)

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:

(B)

Find Chi square statistic.

Chi square statistic 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 statistic  : .

Solution :

(A)

The null hypothesis H₀ : p = 0.5.

The alternate hypothesis H_a : .

(B) Chi square statistic  : .

Answer 2

Step 1:

(C)

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 2:

Reject H₀ if .

Chi square statistic  : .    (From (b))

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 3:

(D)

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

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

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

Solution :

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

(D) The claim that accidents occur more often in the summer is valid.