Question

 The table below is based on records of accidents in 1988 compiled by the Department of Highway Safety and Motor Vehicles in Florida. The analyst would like to know if there is a relationship between Injury type and seatbelts

 a. Would you consider this an experiment? Do you think that these data were collected as part of an experiment? Explain

 b. Give the null and alternative for the test

 c. Use the chi-square test to run the test at a = 0.05

 d. Give the real-world answer

 e. Determine the expected counts for each cell and comment on the validity of the Chi-Square test

Answer 1

The table below is based on records of accidents in 1988 compiled by the Department of Highway Safety and Motor Vehicles in Florida.

The analyst would like to know if there is a relationship between Injury type and seatbelts.

Safety Equipment in Use	Injury
Fatal	Nonfatal
None	1601	162,527
Seat belt	510	412,368

(a).

Would you consider this an experiment? Do you think that these data were collected as part of an experiment? Explain:

No, this is not an experiment.

Yes, this data is collected as part of an experiment. Because they want to know whether there is a relationship between two variables or not.

(b).

Give the null and alternative hypothesis:

Hypothesis:

: Ther is no associations (relation) between injury type and seatbelt.

: Ther is a associations (relation) between injury type and seatbelt

(c).

Use the chi-square test to run the test at =0.05:

Safety Equipment in Use	Injury	Total (Bj)
Fatal	Nonfatal
None	1601 (600.46)	162,527 (163527.53)	164128
Seat belt	510 (1510.53)	412,368 (412368)	412878
Total (Aj)	2111	574895	=577006

Expected from the equation shown in bracket.

Test statistics:

=[4268.72+161532.62+172.19+413366.96]-577006

=579340.49-577006

=2334.49

We, reject at 5% LOS.

(d).

Give the real word answer:

There is a relationship between the injury type and seatbelts i.e,If don't wear seat belt then there is a chance of Fetal injury.

(e).

Determine the expected counts for each cell and comment on the validity of the Chi-Square test:

Here, the expected count of each ell is greater than 5. I.e, Chi-square test assumption is satisfied.

Hence the chi-square test is failed.