Question 1

A sample of 64 account balances of a credit company showed an average balance of $1,125 with a standard deviation of $126.

1. State       your “givens” from the prompt.  
2. What       kind of test will you use, and why?
3. Is       this one-tail, or two tailed, and how do you know?
4. Formulate       the hypotheses that can be used to determine whether the mean of all       account balances is significantly different from $1,200.
5. Compute       the test statistic.  Show your formula and what numbers were plugged       in.
6. Using       the p-value approach, what is your conclusion? Let α = .05.

Question 2

This is a good resource for this problem:  https://stattrek.com/hypothesis-test/difference-in-proportions.aspx?tutorial=ap

p. 485 may also help.
 

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.
 

We  want to determine whether or not the proportions of voters favoring the       Democratic candidate were the same in both states. Provide the hypotheses       (both null and alternative).  Then 

1. Calculate        the proportion of voters in favor of the Democratic Candidate for both        states.
2. I        recommend going to the website above for guidance.  I want to see        the work in calculating the pooled sample proportion and the standard        error.
3. Compute       the test statistic.  Show your work.
4. Determine       the p-value (show your work from the z value to the p value); and at 95%       confidence, test the above hypotheses.
5. State       your results.  Do we reject or fail to reject the null       hypothesis?  Why?

Question 3
 

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered.  The values of 72 and 78 are means.

1. Develop       an interval estimate for the difference between the average yearly       incomes of the marketing managers in the East and West. Use α = 0.05. 
   1. Show        your calculation for the degrees of freedom.
   2. Show        your calculation for the interval estimate – how you plugged the numbers        into the appropriate formula.
2. At       95% confidence, use the p-value approach and test to determine if the       average yearly income of marketing managers in the East is significantly       different from the West.  Show the calculation of p.  Should we       reject or fail to reject the null hypothesis?  Why?

For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadsheet. Download it here.

Using the ROI data set:

1. For       each of the 2 majors test the hypothesis at the 5% significance level: 
   • The        mean ‘Cost’ for a college is $160,000. 
   • List        your givens – n, standard deviation, alpha level
   • Provide        the formula you will use. Why are you using that formula (why does it        fit the situation?)
   • Show        how you have plugged in the numbers.
   • What        is your computed test statistic?
   • Show        the computation of the p value.
   • Will        you reject or fail to reject the null hypothesis? Why?
2. For       Business versus Engineering majors conduct a two sample test of the       hypothesis at the 10% significance level (assume the variances are not       equal): 
   • The        average 30-Year ROI for Business majors is less than for Engineering        Majors.  Be sure to interpret your results.
   • Make        sure you state your givens.
   • State        your null and alternative hypotheses.
   • Show        which formula you used.
   • Why        did you reject or fail to reject your null hypothesis?