i need a clear explanation please. a-e A sample of 500 drivers was askcd whether

Question

i need a clear explanation please.
a-e

A sample of 500 drivers was askcd whether or not they speed while driving. The following table gives a two-way classification: We wish to test whether gender and speeding arc related at the 1% significance level. State the null and alternative hypotheses for this test. Find the critical value for this test. Calculate the test statistic. Should we reject or fail to reject the null hypothesis? Based on your answers to a - d, are gender and speeding likely to bc independent?

Explanation / Answer

a).

Null hypothesis: speed and gender are independent

Alternate hypothesis: speed and gender are not independent ( related)

b).

DF= (r-1)(c-1) = (2-1(2-1) =1

1% level, criticle value = 6.635

c).

Chi-Square Test

Observed Frequencies

speed

never speed

Total

male

222

78

300

female

128

72

200

Total

350

150

500

Expected Frequencies

speed

never speed

Total

male

210

90

300

female

140

60

200

Total

350

150

500

Calculations

fo-fe

12

-12

-12

12

(fo-fe)^2/fe

0.6857

1.6000

1.0286

2.4000

Chi-Square Test Statistic

= 5.714

d).

Calculated chi square =5.714 < 6.635 the table value

Null hypothesis is not rejected

e).

We conclude that gender and speeding are independent.

Chi-Square Test

Observed Frequencies

speed

never speed

Total

male

222

78

300

female

128

72

200

Total

350

150

500

Expected Frequencies

speed

never speed

Total

male

210

90

300

female

140

60

200

Total

350

150

500

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