compute the expected counts for the day of the week and show how you got it plea

Question

compute the expected counts for the day of the week and show how you got it please.

also what is the test statistic?

and what is the p-value?

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 n 314 randomly selected accidents. ls there reason to believe that the accident ooours with equal frequency with respect to the day of the week at the 0.05 level of significance? Click the icon to view the table. Let P the proportion of accidents on day i, where i -1 for Sunday, i -2 for Monday, etc. What are the null and alternative hypotheses? H,: More accidents occur later in the week than earlier B. Ho: At least one proportion is different from the others C. Ho: P1-P2-... = P7 = H,: More accidents occur earier in the week than later H,: At least one proportion is different from the others Compute the expected counts for day of the week. of the Week Observed Count Expected Count Sunday Monday Tuesday 43 43 31 39 Thursday Friday 52 62 to two decimal olaces as needed.) Enter your answer in the edit fields and then click Check Answer. Check Answer remaining

Explanation / Answer

ChiSquare Test For INDEPENDENCE TEST

observed frequncies are Oi

43 43 31 39 44 52 62   

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expected frequencies are Ei

314/7 = 44.8571

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and claiming hypothesis is

null, Ho: p1=p2=...=1/7

alternative, H1: atleast one proportion is diffrent from others

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =5.9915

since our test is right tailed,reject Ho when ^2 o > 5.9915

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table take sum of (Oi-Ei)^2/Ei, we get ^2 o = 12.9045

critical value

the value of |^2 | at los 0.05 with d.f, n - 1 = 3 - 1 = 2 is 5.9915

we got | ^2| =12.9045 & | ^2 | =5.9915

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0.0016

ANSWERS

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null, Ho: p1=p2=...=1/7

alternative, H1: atleast one proportion is diffrent from others

test statistic: 12.9045

critical value: 5.9915

p-value:0.0016

decision: reject Ho

Observed (Oi ) Expected ( Ei) Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 43 44.8571 -1.86 3.4488 0.0769 43 44.8571 -1.86 3.4488 0.0769 31 44.8571 -13.9 192.019 4.2807 39 44.8571 -5.86 34.3056 0.7648 44 44.8571 -0.86 0.7346 0.0164 52 44.8571 7.143 51.021 1.1374 62 44.8571 17.14 293.879 6.5514

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