Question

In: Statistics and Probability

Two internet companies, Accelerate and Speedy, are the only two companies that provide internet service to...

Two internet companies, Accelerate and Speedy, are the only two companies that provide internet service to households in the area.   The companies offer different internet speeds and hence it affects web page loading times.   

  • The web page loading times for internet service provided by Accelerate are normally distributed with a mean of 15 seconds and a standard deviation of 3.5 seconds.  
  • The web page loading times for internet service provided by Speedy are uniformly distributed from 18 seconds to 38 seconds.  

You are visiting a houshold in the area and you want to know who their internet provider is, Accelerate or Speedy, that is, to test the competing hypotheses:

H0: The internet provider is Accelerate versus Ha: The internet provider is Speedy.

You plan to use the following Decision Rule:
If a web page loading time takes more than 23 seconds, you will decide the internet service provider is Speedy (Ha),
but if a web page loading time takes less than 23 seconds, you will decide the internet service provider is Accelerate (H0).

Question 8 Subquestions

8.a

TBD points

Compute the level of significance of the hypothesis test, showing all relevant work.

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8.b

TBD points

Find the p-value for an observation of a web-page loading speed of 25 seconds, showing all relevant work.

8.c

TBD points

You observe a web page loading time of 25 seconds. Use the information given to:
1) Make a decision and conclusion about which internet provider, Accelerate or Speedy, you think this household uses, based on the Decision Rule and your observation of 25 seconds.

2) Using the significance level you found in part a and the p-value you found in part b, make a decision and conclusion and which internet provider, Accelate or Speedy, you think this household uses.

3) Do your decisions and conclusions in Steps 1 and 2 match?

8.d

TBD points

Find the power of this hypothesis test, showing all relevant work.

8.e

TBD points

Provide one recommendation that would increase the power of this hypothesis test.

Solutions

Expert Solution

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