Question

Task: Apply mathematical problem solving skills to a variety of problems at the college level.

To accomplish this task, the students will

1. Identify what they are given and what they need to find;

2. Identify the type of problem they have been given and the tools necessary to solve the problem;

3. Correctly apply the tools to the information given to set up the problem;

4. Perform mathematically correct calculations to determine a solution;

5. Interpret their results in terms of the original problem.

The written work for the following problem must be submitted to receive credit. The formulas and numbers that have been used in the formula must be shown to receive credit.

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank’s claim. Use the information given below. State the null and alternative hypotheses, the significance level, the critical value, the test statistic, the decision and conclusion. All work must be written out and shown.

Sample statistics for a local bank and a competitor's bank

  

Local Bank Competitor Bank   

Sample size Local Bank: n1=46 , Competitor bank: n2=50

Average waiting time in minutes for each sample Local Bank: X¯1=2.3 mins. (line should be above X), Competitor Bank X¯1=2.6 mins.(line should be above X)

Sample Standard Deviation of each Sample Local BankL s1= 1.1 mins, Competitor Bank:s2=1.0 mins

1. Are the samples dependent or independent?
2. State your Null/Alternative hypotheses
3. What is the test-statistic?
4. What is the p-value?
5. What are the critical values?
6. Does the test-statistic lie in the rejection region?
7. Interpret the Result?
8. Does the result change for a different value of alpha? Explain?

Answer 1