A recent sample of adults was asked their opinions regarding government spending

Question

A recent sample of adults was asked their opinions regarding government spending on health and government spending on law enforcement. The data are in the table below.

Law Enforcement Spending

Health Spending

Increase

Decrease

Total

Increase

292

25

317

Decrease

14

9

23

Total

306

34

340

Test whether increased spending is favored in one area. Use a 5% level of significance.  1) Write out the appropriate null hypothesis and the alternative hypothesis; 2) Calculate the test statistic (show your work); 3) Give your conclusion including a comparison to alpha or the critical value.

Law Enforcement Spending

Explanation / Answer

1)here null hypothesis: Ho: Health spending is not favourable

Alternate hypothesis:Ha: Health spending is favourable in one direction

2)here critical value for one degree of freedom and 5% level =3.8415

from above chistat =23.259 which is higher then critcal value hence we reject null hypothesis in favour of alternate hypothesis.

also for above chi stat p value =0.0000

whcih is lower then 0.05 level ; hence we reject null hypothesis.

Observed O Increase Decrease Total Increase 292 25 317 Decrease 14 9 23 Total 306 34 340 Expected E=rowtotal*column total/grand total Increase Decrease Total Increase 285.300 31.700 317 Decrease 20.700 2.300 23 Total 306 34 340 chi square =(O-E)^2/E Increase Decrease Total Increase 0.157 1.416 1.573 Decrease 2.169 19.517 21.686 Total 2.326 20.933 23.259

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