Car Seat Safety Case Researchers wish to simulate the safety of the market-leadi
ID: 3150415 • Letter: C
Question
Car Seat Safety Case Researchers wish to simulate the safety of the market-leading child car seat. Their test consists of placing the maximum claimed weight in the car seat and simulating crashes at higher and higher miles per hour until a problem occurs. Analyze the he Car Seat Excel file to determine necessary values. Use analysis and construct 95 percent confidence interval for the population mean speed at which a problem with the car seat first appears. Assume normality.
Are we 95 percent confident that this population mean is at least 30 mph?
Results of Car Seat Safety Tests
Car: Seat Speed
1: 31
2: 29.4
3:30.4
4: 28.9
5: 29.7
6: 30.1
7 :32.3
8 :31.7
9: 35.4
10: 29.1
11:: 31.2
12 :30.2
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 30
Ha: u > 30
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 11
tcrit = + 1.795884819
Getting the test statistic, as
X = sample mean = 30.78333333
uo = hypothesized mean = 30
n = sample size = 12
s = standard deviation = 1.786226766
Thus, t = (X - uo) * sqrt(n) / s = 1.519149929
Also, the p value is
p = 0.078465612
As t < 1.796, and P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the population mean is at least 30 mph at 0.05 level. [CONCLUSION]
*************************************
For the lower confidence interval:
Note that
Lower Bound = X - t(alpha) * s / sqrt(n)
where
alpha = (1 - confidence level) = 0.05
X = sample mean = 30.78333333
t(alpha) = critical t for the confidence interval = 1.795884819
s = sample standard deviation = 1.786226766
n = sample size = 12
df = n - 1 = 11
Thus,
Lower bound = 29.85730463
Thus, the confidence interval is
u > 29.85730463 [ANSWER, LOWER CONFIDENCE BOUND]
As part of this interval is below 30, then there is no significant evidence that the population mean is at least 30 mph at 0.95 confidence. [CONCLUSION]