Medical practitioners are increasingly utilising the Zoom platform. Not only for online meetings but also for consultations with patients. The weekly Zoom access time (in hours) at two hospitals: Health Care I  Health Care II  needs to be investigated. Given: The weekly access time of medical practitioners at both hospitals is normally distributed with a standard deviation of σ=6 hours. a) Consider the weekly access time at Health Care I Given:  X= the weekly access time of a medical practitioner. The mean weekly access time is μ=20 hours. Complete the following: (Round your answers to 4 decimal places.) The probability that the weekly access time of a randomly selected medical practitioner is between 13 and 27 hours is: _______ Only 10% of the medical practitioners had a weekly access time of ______ hours or more. Given:  X¯= the average weekly access time of a random sample of n=20 medical practitioners.  The standard error of X¯ is σX¯=1.3416 Complete the following: (Round your answers to 4 decimal places.) Ninety-five percent of the average weekly access times are within ________ hours of the mean μ=20 The probability that X¯ is at least 21.7 hours is: _______ b) Consider the weekly access time at Health Care II

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Medical practitioners are increasingly utilising the Zoom platform. Not only for online meetings but also for consultations with patients. The weekly Zoom access time (in hours) at two hospitals:

  • Health Care I 
  • Health Care II 

needs to be investigated.

Given: The weekly access time of medical practitioners at both hospitals is normally distributed with a standard deviation of σ=6 hours.

a) Consider the weekly access time at Health Care I

Given: 

  • X= the weekly access time of a medical practitioner.
  • The mean weekly access time is μ=20 hours.

Complete the following: (Round your answers to 4 decimal places.)

  • The probability that the weekly access time of a randomly selected medical practitioner is between 13 and 27 hours is: _______
  • Only 10% of the medical practitioners had a weekly access time of ______ hours or more.

Given:

  •  X¯= the average weekly access time of a random sample of n=20 medical practitioners.
  •  The standard error of X¯ is σX¯=1.3416

Complete the following: (Round your answers to 4 decimal places.)

  • Ninety-five percent of the average weekly access times are within ________ hours of the mean μ=20
  • The probability that X¯ is at least 21.7 hours is: _______

b) Consider the weekly access time at Health Care II

The Superintendent wants to investigate the average weekly access time (in hours) at Health Care II based on 2 different research questions. A random sample of the weekly access times of n=20 medical practitioners revealed an average of x¯=25.09 hours.

Let: μ= mean weekly access time of the medical practitioners.

Research Question 1: Is the mean weekly access time less than 28 hours?

Given: The value of the test statistic is

z=−2.17

Complete the following:

  • Identify the correct null hypothesis

     

    • H0:μ>25.09
    • H0:x¯=25.09
    • H0:x¯≠25.09
    • H0:μ=28
    • H0:x¯>28
    • H0:x¯=28
    • H0:μ<28
    • H0:x¯<28
    • H0:μ≠28
    • H0:x¯>25.09
    • H0:μ<25.09
    • H0:μ≠25.09
    • H0:x¯<25.09
    • H0:μ>28
    • H0:μ=25.09
    • H0:x¯≠28
  • The p-value is: _________ Round your answer to 4 decimal places. 

Research Question 2: Does the mean weekly access time differ from 24 hours?

Given: The 99% confidence interval for  μ is:

(21.6,28.5)
 

 

Complete the following:

  • According to the observed confidence interval, the null hypothesis is _______ (rejected/not rejected) and there is sufficient evidence to claim that the average access time ______ (differs/does not differ)   from 24 hours, at 0.01 level of significance.
  • According to the observed confidence interval, we know that:

     

      True False
    For every 100 random samples drawn, we expect that  99 of the confidence intervals will contain the population mean.    
    99% of all samples should have sample means between 21.6 and 28.5    
    We are 99% confident that μ is between 21.6 and 28.5    
    For every 100 random samples drawn, we expect that  99 of the confidence intervals will contain the sample mean.    
    The probability that μ is between 21.6 and 28.5 is 0.99    
    99% of all medical practitioners at Health Care II have access times between 21.6 and 28.5 hours.
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a)

Given information:

The weekly access time of medical practitioners at both hospitals is normally distributed with a standard deviation of σ = 6 hours.

X = the weekly access time of a medical practitioner.

The mean weekly access time is μ = 20 hours.

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