Question

In: Statistics and Probability

The use of cellular phones in automobiles has increased dramatically in the last few years. Of...

The use of cellular phones in automobiles has increased dramatically in the last few years. Of concern to traffic experts, as well as manufacturers of cellular phones, is the effect on accident rates. Is someone who is using a cellular phone more likely to be involved in a traffic accident? What is your conclusion from the following sample information? Use the 0.05 significance level.

	Had Accident in the Last Year	Did Not Have an Accident in the Last Year
Uses a cell phone	46	404
Does not use a cell phone	19	268

Click here for the Excel Data File

H₀: There is no relationship between phone use and accidents.

H₁: There is a relationship between phone use and accidents.

State the decision rule using 0.05 significance level. (Round your answer to 3 decimal places.)

Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H₀?

Expert Solution

Significance level : =0.05

Degrees of freedom = (Number rows-1) x (Number of columns-1)=(2-1)x(2-1)=1

Critical value of for 1 degree of freedom = 3.841

If value of the test statistic is greater than the critical value : 3.841 ; Reject the null hypothesis; Otherwise fail to reject the null hypothesis.

Test Statistic

O : Observed Frequency

E: Expected Frequency

Observed Counts/Frequency	Had Accident in the Last Year	Did Not Have an Accident in the Last Year	Row Total
Uses a cell phone	46	404	450
Does not use a cell phone	19	268	287
Column Total	65	672	Grand Total =737

E: Expected Count/Frequency	Had Accident in the Last Year	Did Not Have an Accident in the Last Year
Uses a cell phone	(450*65) / 737	(450*672) / 737
Does not use a cell phone	(287*65) / 737	(287*672) / 737

E: Expected Count/Frequency	Had Accident in the Last Year	Did Not Have an Accident in the Last Year
Uses a cell phone	39.6879	410.3121
Does not use a cell phone	25.3121	261.6879

O	E	O-E
46	39.6879	6.3121	39.8423	1.0039
404	410.3121	-6.3121	39.8423	0.0971
19	25.3121	-6.3121	39.8423	1.5740
268	261.6879	6.3121	39.8423	0.1523

value of chi-square = 2.827

As value of the test statistic: 2.827 < the critical value : 3.841 ; fail to reject the null hypothesis.

There is not sufficient evidence to conclude that There is a relationship between phone use and accidents.

Therefore,

Is someone who is using a cellular phone more likely to be involved in a traffic accident? No evidence with the given data.

orchestra answered 2 years ago

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