[Answered] Math 215: Application Assignment

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Week 9 – Application Assignment

 

Part 1) CHARITABLE GIVING (8 pts)

You are the manager of an internal charitable giving campaign at a non-profit organization. The board of the organization has agreed to match the employee donations this year if you can inspire the employees to create enough workplace goodwill that more than 70% of employees in the organization increase their level of participation in the campaign this year.  A random sample of post-campaign data shows that 43 of 51 employees have increased their giving this year. Present your findings to the board, and if more than 70% of employees increased their participation of charitable giving this year hold the board accountable for their promise of matching the donations. Perform a hypothesis test following the steps below (Use  = 0.10).

 

  1. What is the name of the type of hypothesis test required here?
  2. Is this a left-tailed, right-tailed, or two-tailed test?

 

  1. State AND verify all assumptions required for this test.

[HINT: This test should have four assumptions to be verified.]

 

  1. State the null and alternate hypotheses for this test: (use correct symbols and format!)

 

Null hypothesis

Alternate hypothesis

  1. Run the correct hypothesis test and provide the information below. Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

 

Test Statistic

Critical value [HINT: this is NOT ]

p-value

 

  1. State your statistical decision (and justify it!)
  2. Interpret your decision within the context of the problem. What is your conclusion?

 

 

 

 

 

 

 

 

 

Part 2) URGENT CARE (8 pts)

You recently started working as a nurse manager at a larger local urgent care facility.  Because the center is so new (and a bit fancier than most) many patients come here expecting a bit of a wait before they can be seen.  Out of curiosity, on a particularly busy day you write down how many minutes a random sample of patients has to wait before being seen by one of the medical staff.

Using a significance level of 0.05, test whether the average wait time is less than 15 minutes.

 

12 10 15 17 15 18 15 15
10 15 12 10 12 19 10 14
10 17 13 15 23 12 15 20
7 10 16 14 14 14 18 13

 

  1. What is the name of the type of hypothesis test required here?
  2. Is this a left-tailed, right-tailed, or two-tailed test?

 

  1. State AND verify all assumptions required for this test.

[HINT: This test has two assumptions.]

 

  1. State the null and alternate hypotheses for this test: (use correct symbols and format!)

 

Null hypothesis

Alternate hypothesis

  1. Run the correct test in Excel or on the TI-84 calculator and provide the information below. For each statistic provide the correct symbol and numeric value (round answers to 3 decimal places).

 

Degrees of Freedom

Test Statistic

Critical Value

p-value

 

  1. State your statistical decision for this test and justify it using the statistics above.

 

  1. Interpret your decision within the context of the problem. What is your conclusion?

 

 

 

Solution

  1. What is the name of the type of hypothesis test required here? The level of participation in the campaign refers to a population proportion, thus we must test the conditions necessary to use the normal distribution. The non-profit organisation does a post-campaign data sample of 51 employees, so n=51, and level of participation is 70%, so p=0.7. Therefore, we can calculate the following.

np=35.7 ≥ 10

n(1-p) =15.3 ≥ 10

All of the conditions are met, so the non-profit organisation should use the Normal distribution to test its claim which is z distribution hypothesis test.

 

  1. Is this a left-tailed, right-tailed, or two-tailed test?

    This is a right-tailed test……………………Purchase the link to access the full answer @$10