Question

1. An operations manager at a factory that produces rechargeable batteries for smart phones wants to determine if the new brand of battery that they are producing is superior to their original design.

	Sample	Average Life	Standard Dev.
Old	25	6.5 hours	1.25 hours
New	35	7.2 hours	0.75 hours

Using a 0.01 level of significance and assuming equal variances, identify the alternative hypothesis to these the claim that the new brand of batteries is superior to the original design. For the calculations, use "New-Old"
a) Ha: u_N - u_O > 0
b) Ha: u_N - u_O ≤ 0
c) Ha: u_N - u_O ≠ 0
d) Ha: u_D > 0

2. Calculate the pooled variance (s²_P). Round your answer to two decimal places.

3. Calculate the test statistic. Round your answer to two decimal places.

4. Calculate the effect size. Round your answer to two decimals.

Answer 1

let sample 1 be new and sample 2 be old.

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 >   0
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1)

a) Ha: uN - uO > 0

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Level of Significance ,    α =    0.01
     

new-
mean of sample 1,    x̅1=   7.2000
standard deviation of sample 1,   s1 =    0.7500
size of sample 1,    n1=   35

old ---   

mean of sample 2,    x̅2=   6.5
standard deviation of sample 2,   s2 =    1.25
size of sample 2,    n2=   25
      
difference in sample means =    x̅1-x̅2 =    0.7000
      
pooled variance Sp²=   ([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) = 0.98

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3)

std error , SE =    √(Sp²/n1+Sp²/n2) =    0.2587
      
t-statistic =    ((x̅1-x̅2)-µd)/SE =    2.71

p-value =        0.0045 [from t table
Conclusion:     p-value <α=0.01 , Reject null hypothesis  

so, there is enough evidence that  new brand of batteries is superior to the original design at α=0.01

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4)effect size ,

Cohen'D = | (x1 bar - x2 bar ) / √Sp² | = |(7.2-6.5)/√0.98 | = 0.71