Project #121291 - Paper Assignments Statistics on (MiniTab)

 Chapter 9 On-Paper Assignments

(20 points, each question = 10 pts.)

Begin each problem by re-writing the problem. Minitab is required; attach or include your output. Use Word; you may handwrite equations. You may want to refer to the Minitab handouts for Chapter 9 (on Canvas under Modules, Chapter 9 Handouts).

  1. The data below represents the amount that a sample of fifteen customers spent for lunch ($) at a fast-food restaurant:

7.42   6.29   5.83   6.50   8.34   9.51   7.10   6.80   5.90   4.89   6.50   5.52   7.90   8.30   9.60

  1. At the 0.05 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50? Follow and show the 7 steps for hypothesis testing.
  2. Determine the p-value and interpret its meaning.
  3. What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid?  Use and include an appropriate graph from Minitab.  Write a couple of sentences supporting your answer.
  4. Verify your results using Minitab.

 

  1. Of 800 surveyed active LinkedIn members, 327 reported that they are planning to spend at least $1,000 on consumer electronics in the coming year.
  2. At the 0.05 level of significance is there evidence that the proportion of all LinkedIn members who plan to spend at least $1,000 on consumer electronics is different from 35%? Follow and show the 7 steps for hypothesis testing.
  3. Determine the p-value and interpret its meaning.
  4. What assumption must you make in order to conduct the test in part a? Demonstrate if the assumption is met.
  5. Verify your results for parts a and b using Minitab.

 

 

__________________________________________________________________________________________________

Example[1]:  A bank brank has located in a commercial district of a city with the business objective of improving the process for servicing customer during the noon-to-1:00 P.M. lunch period.  The waiting time (operationalized as the time the customer enters the line until he or she is reaches the teller window) of all customers during their hour is recorded over a period of a week.  Data were collected from a random sample of 15 customers, and the results are organized as follows:

Waiting Time

   4.21   5.55   3.02   5.13   4.77   2.34   3.54   3.20   4.50   6.10   0.38   5.12   6.46   6.19   3.79

 

Research Questions:

  1. At the 5% level of significance, is there evidence that the population mean waiting time is less than 5 minutes?
  2. What assumption about the population distribution is needed in order to conduct the hypothesis test? Is the assumption valid?  Provide evidence to support your answer.

 

Format for Turn-in Assignments

Begin each problem by writing the problem as written or given in the textbook, etc.  Then follow the following steps to hypothesis testing:

Steps to hypothesis testing:

  1. State the research question or objective.
  2. Formulate the null and alternative hypotheses.
  3. Choose a significance level.
  4. Determine the appropriate test statistic and its distribution. Determine the critical area (and critical values).  State the Decision Rule.
    1. In terms of critical values OR
    2. In terms of the p-value
  5. Calculate the test statistic (and p-value).
  6. Make a decision by comparing the test statistic to the critical value OR comparing the p-value to alpha.
    1. Reject Ho
    2. Fail to reject Ho
  7. Give a brief but thorough conclusion.

 

 

Restate Question or Problem

A bank brank has located in a commercial district of a city with the business objective of improving the process for servicing customer during the noon-to-1:00 P.M. lunch period.  The waiting time (operationalized as the time the customer enters the line until he or she is reaches the teller window) of all customers during their hour is recorded over a period of a week.  Data were collected from a random sample of 15 customers, and the results are organized as follows:

Waiting Time

   4.21   5.55   3.02   5.13   4.77   2.34   3.54   3.20   4.50   6.10   0.38   5.12   6.46   6.19   3.79

 

Research Questions:

  1. At the 5% level of significance, is there evidence that the population mean waiting time is less than 5 minutes?
  2. What assumption about the population distribution is needed in order to conduct the hypothesis test? Is the assumption valid?  Provide evidence to support your answer.

Step 1:  State the research question or objective.  At the 5% level of significance is there evidence that the population mean waiting time is less than 5 minutes?

Step 2:  Formulate the null and alternative hypotheses.

;

Step 3:  Choose a significance level.

Significance level (a) = 0.05.

Step 4:  Determine the appropriate test statistic and its distribution.  State the Decision Rule.

The test statistic is , since population standard deviation, s, is unknown

Decision Rule (D.R.):   Reject Ho if p-value < 0.05 (a)

Step 5:  Calculate the test statistic and its p-value

From Minitab:     = – 1.6867, p-value = 0.057

Step 6:  Decision.  Using the Decision Rule, compare p-value to a  and make a decision.

Fail to reject Ho since p-value of 0.057 is not less than a of 0.05.

Step 7:  Written Conclusion.  Compare the decision to the hypotheses and write the conclusion.

At the 5% level of significance there is insufficient evidence that the mean population waiting time is less than 5 minutes. 

Managerial implications:  The business objective to improve waiting time indicates insufficient evidence that the waiting time has been significantly reduced.  Thus, this process to improve waiting time did not meet the objective.

Answers:

  1. a) At the 5% level of significance there is insufficient evidence (= – 1.6867, p-value = 0.057) that the mean population waiting time is less than 5 minutes.
  2. b) From the histogram (or boxplot) of the sample data, it appears that the population may not be quite normally distributed. However, since the t-distribution is fairly robust with respect to the Normality Assumption, the results are deemed valid. 

 

 

[1] Adapted from problem 9.74, page 357 from Basic Business Statistics:  Concepts and Applications, 12thedition, by Berenson, Levine, and Krehbiel, Prentice Hall, 2012.

 

Subject Business
Due By (Pacific Time) 04/14/2016 10:00 am
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