A recent sample of adults was asked their opinions regarding government spending
ID: 3178917 • Letter: A
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