Car Seat Safety Case Researchers wish to simulate the safety of the market-leadi

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]

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