In a study conducted by Edgar Snyder & Associates, 85 % of adults in Pennsylvani
ID: 3259953 • Letter: I
Question
In a study conducted by Edgar Snyder & Associates, 85 % of adults in Pennsylvania wore seatbelts in 2010. In a survey done in 2010, 700 adults were asked if they wear their seatbelt.
a) Find the mean and standard deviation for the number of people that actually wear their
seatbelt in the group of 700, round to the nearest tenths.
b) In the survey 700 subjects, 627 claimed that they do indeed wear their seatbelt. Is this result consistent with the study, or is the result unlikely to occur with an actual seatbelt usage percent of 85 %? Justify your response.
Explanation / Answer
a)
mean = n p = 0.85 * 700 = 595
standard deviation = Sqrt(np(1-p))
= sqrt(700 * 0.85 * 0.15)
= 9.4472
b)
H0: Po = 0.85 , Po > 0.85
p = 627 /700 = 0.8957
test statistics.
p - Po / sqrt ( Po(1-Po)/n)
0.8957 - 0.85 / Sqrt(0.85*0.15 / 700)
0.0457/0.0135
3.3862
At 95% confidence level, critical value is 1.6449.
Since test statistics value > Critical value, we have sufficient evidence to reject H0.
WE conclude that 627 out of 700 people do indeed wear their seatbelt.