Question

A researcher wanted to determine whether certain accidents were uniformly distributed over the days of the week. The data show the day of the week for nequals303 randomly selected accidents. Is there reason to believe that the accident occurs with equal frequency with respect to the day of the week at the alphaequals0.05 level of​ significance?

Answer 1

Chi-square = 4.600

Degrees of freedom= 6

there is no evidence to reject hypothesis.

Explanation:

H₀ : uniformly distributed

H₁: not uniformly distributed

Suppose some value of observed or expected frequency

Observed frequency : 39 40 30 40 41 49 41 Total: 280

Expected frequency : 40 40 40 40 40 40 40 Total: 280

Calculated the chi-square value

Chi-square = sigma {(O-E)^2/E}

= 0.025+0.000+2.500+0.000+0.025+2.025+0.025

4.600

Degrees of freedom=d f = n-1 = 7-1 = 6

Chi-square for 6 d.f at alpha = 0.05 is 12.59

Chi-square of calculated value < its critical value at alpha = 0.05, we see that there is no evidence to reject hypothesis.

The frequency of Sat is wrongly taken as 41 instead of 51