A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts. The following is the setup for this hypothesis test: H0:p=0.65
Ha:p<0.65
In this example, the p-value was determined to be 0.277. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Select the correct answer below:
A. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
B. There is NOT sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
C. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 35%.
D. There is NOT sufficient evidence to conclude that the pronortion of people wearing seat belts is less than 35%

Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%

Step-by-step explanation:

The police officers claim is that the proportion of people wearing seat belts is less than 65%.

Now, we are told that the p - value is 0.277.

In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.

Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.

So the correct option is A.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west