13. A phone manufacturer wants to compete in the touch screen phone market. Mana

Question

13. A phone manufacturer wants to compete in the touch screen phone market. Management understands that the leading product has a less than desirable battery life. They aim to compete with a new touch phone that is guaranteed to have a battery life more than two hours longer than the leading product. A recent sample of 120 units of the leading product provides a mean battery life of 5 hours and 40 minutes with a standard deviation of 30 minutes. A similar analysis of 100 units of the new product results in the mean battery life of 8 hours and 5 minutes and a standard deviation of 55 minutes. It is not reasonable to assume that the population variances of the two products are equal.

a. Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product.

b. Implement the test at the 5% significance level using the critical value approach.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   2  
Ha:   u1 - u2   >   2  

b)

At level of significance =    0.05          
As we can see, this is a    right   tailed test.

Calculating the means of each group,              
              
X1 =    5.666666667          
X2 =    8.083333333          
              
Calculating the standard deviations of each group,              
              
s1 =    0.5          
s2 =    0.916666667          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    120          
n2 = sample size of group 2 =    100          
Thus, df = n1 + n2 - 2 =    218          
Also, sD =    0.102401714          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -43.13078831          
              
where uD = hypothesized difference =    2          
              
Now, the critical value for t is              
              
tcrit =        1.651873373      
              
Thus, comparing |t| > 1.6519, , WE REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that the new touch phone has a battery life more than two hours longer than the leading product. [CONCLUSION]

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