Two internet companies, Company X and Company Y, are the only two companies that

Question

Two internet companies, Company X and Company Y, 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 Company X are normally distributed with mean of 20 seconds and a standard deviation of 5 seconds.  

The web-page loading times for interenet service provided by Company Y are uniformly distributed from 25 seconds to 60 seconds.  

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

H0: The internet provider is Company X   versus Ha: The internet provider is Company Y.

You plan to use the following decision rule:
If a web-page loading time takes more than 30 seconds, you will decide the internet service provider is Company Y (Ha),
but if a web-page loading time takes less than 30 seconds, you will decide the internet service provider is Company X (H0).

For this situation, determine the level of significance for this test? (select one)

1) 0.975

2) 0.95

3) 0.8571

4) 0.1429

5) 0.05

6) 0.025

Find the power of this test? ( select one)

1) 0.975

2) 0.95

3) 0.8571

4) 0.1429

5) 0.05

6) 0.025

For this situation, find the value of ? (select one)

1) 0.975

2) 0.95

3) 0.8571

4) 0.1429

5) 0.05

6) 0.025

Explanation / Answer

1)

  level of significance: =probability time is greater than 30

option 6

2)

power of this test: =P(rejecting when company Y) =P(Y>30)= (60-30)/(60-25)=30/35 =0.8571 option 3

3) =1-power =1-0.8571 =0.1429 option 4

for normal distribution z score =(X-)/ here mean=       = 20.000 std deviation   == 5.0000

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