business
μ_{1} is the population mean for individuals with a CFA designation and μ_{2} is the population mean of individuals with MBAs 
a.  Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.  

b1.  Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places) 
Test statistic 
b2.  Calculate the critical value at the 1% level of significance. (Negative value should be indicated by a minus sign.Round your answer to 3 decimal places.) 
Critical value 
b3.  Do you reject the null hypothesis at the 1% level?  

c.  Using the critical value approach, can we reject the null hypothesis at the 10% level?  

3.
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 a 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. Let new products and leading products represent population 1 and population 2, respectively. Use Table 2. 
Sample 1 is from the population of new phones and Sample 2 is from the population of old phones. All times are converted into minutes. 
a.  Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product.  

b1.  Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) 
Test statistic 
b2.  Implement the test at the 5% significance level using the critical value approach.  

4.
Consider the following competing hypotheses: Use Table 2. 
H_{0}: μ_{D} ≥ 0; H_{A}: μ_{D} < 0 
dbar = −2.8, s_{D} = 5.7, n = 12 
The following results are obtained using matched samples from two normally distributed populations: 
a.  At the 5% significance level, find the critical value(s). (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) 
Critical value 
b.  Calculate the value of the test statistic under the assumption that the difference is normally distributed.(Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) 
Test statistic 
c.  What is the conclusion to the hypothesis test?  

5.
Consider the following matched samples representing observations before and after an experiment. Assume that sample data are drawn from two normally distributed populations. Let the difference be defined as Before minus After. Use Table 2. 
Before  2.5  1.8  1.4  −2.9  1.2  −1.9  −3.1  2.5 
After  2.9  3.1  3.9  −1.8  0.2  0.6  −2.5  2.9 

Click here for the Excel Data File 
a.  Construct the competing hypotheses to determine if the experiment increases the magnitude of the observations.  

b1.  Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) 
Test statistic 
b2.  Approximate the pvalue.  
