Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the occupants not wearing seat belts and occupants wearing seat belts. The population proportion of occupants not wearing seat belts and occupants wearing seat belts would be p1 and p2 respectively.
P1 - P2 = difference in the proportion of occupants not wearing seat belts and occupants wearing seat belts.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 > p2
p1 - p2 > 0
it is a right tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples.
For occupants not wearing seat belts,
x1 = 31
n1 = 2823
P1 = 31/2823 = 0.011
For occupants wearing seat belts,
x2 = 16
n2 = 7765
P2 = 16/7765 = 0.0021
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (31 + 16)/(2823 + 7765) = 0.0044
1 - pc = 1 - 0.0044 = 0.9956
z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.011 - 0.0021)/√(0.0044)(0.9956)(1/2823 + 1/7765) = - 0.0089/0.00145462023
z = 6.81
From the normal distribution table,
p < 0.00001
0.00001 < 0.05, we would reject the null hypothesis.
Therefore,
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities
