Studies from past few years of Drexel university students sh

Studies from past few years of Drexel university students showed that the time students spend on internet (including social media, email, downloads, searches, etc.) each week averages to 23.5 hours, with a standard deviation of 4.5 hours. Assuming these values are the population parameters, find the probability that average of a sample of 100 new students from Drexel University will be more than 25.5 hours of internet usage per week.                   

Patient First, Inc., a major long term care company claims that it saves an average of more than $250 per patient per month by using the company

Solution

So the probability that average of a sample of 100 new students from Drexel University will be more than 25.5 hours of internet usage per week is

P(xbar>25.5) = P((xbar-mean)/(s/vn) >(25.5-23.5)/(4.5/sqrt(100)))

=P(Z>4.44) = 0 (from standard normal table)

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What are the hypotheses is the HMO will be testing?         

Let mu be the population mean

Null hypothesis: mu=250

Alternative hypothesis: mu>250

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What is the Type I error in this case?    

Type I error: We reject the null hypothesis when it is true.

We reject that it saves an average $250 per patient per month by using the company