I have Statistics 1000, which is a first year university course exam going on right now. I need someone to finish it in 2 hours and stay connected with me as I will copy and paste each question so I n

Question 28

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Question 1 [7 marks].  A sample of Alzheimer's patients is tested to assess the amount of time in stage IV sleep these patients get in a 24-hour period. Number of minutes spent in Stage IV sleep is recorded for 61 patients. The mean stage IV sleep over a 24 hour period of time for these 61 patients was 48 minutes with a standard deviation of 14 minutes.

(a)     Compute 95% confidence interval for mean stage IV sleep. Interpret this confidence interval. (2 marks)

(b) It has been believed that individuals suffering from Alzheimer's Disease may spend less time per night in the deeper stages of sleep. Test the hypothesis at 5% significance level if the true mean stage IV sleep of Alzheimer patients is less than 50 minutes.

1. Provide the hypothesis statement  (1 Marks)

2. Calculate the test statistic value (2 Marks)

3. Determine the probability value (1 Marks)

 (c) Could the confidence interval in part (a) be used to test the hypothesis in part (b)? Why or why not? (1 mark)

Note: if you need to use symbols  please you

• "u" for population mean "μ", 

• Ho and Ha for  for the null and alternate hypothesis,

•  "Y-hat" for "ŷ", 

• "alpha" for α

Please provide your answers to the above questions by typing your answers using simple text. You need not show the work in detail.

Question 29

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Long answer question [6  marks]

Motorists travelling at higher rates of speed or driving too fast for conditions have less time to react, take longer to stop in an emergency, and don’t always see warning and advisory signs. The faster your speed, the more distance you need to stop. It increases even more in wet or icy road conditions.  Following tables shows the speed of a vehicle and total stopping distance (reaction + braking) in ideal weather condition. It is determined that approximately 98.77% of the variation in the total stopping distance can be explained by the variation in the speed.

(a)   Determine the five-number summary of the Total Stopping Distance. (1 mark)

(b)   Determine if the Total Stopping Distance contains outliers (2 marks).

(c)    Calculate the least squares regression equation for predicting the Total Stopping Distance from the speed of a vehicle. (2 marks)

(d)   Calculate the residual if the speed of your vehicle is 70 km/h. (1 mark)

Note: if you need to use symbols , please use

• "u" for population mean "μ", 

• Ho and Ha for  for the null and alternate hypothesis,

• "Y-hat" for "ŷ", "alpha" for α
  Please provide your answers to the above questions by typing your answers using simple text. You need not show the work in detail.

Question 30

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Long answer question [5 marks]

Winnipeg district sales manager of Far End Inc. a university textbook publishing company, claims that the sales representatives makes an average of 40 calls per week on professors. Several representatives say that the estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42 and variance is 4.41.

Conduct an appropriate hypothesis test, at the 5% level of significance to determine if the mean number of calls per salesperson per week is more than 40.

(a)     Provide the hypothesis statement  (1 Marks)
(b)     Calculate the test statistic value (2 Marks)
(c)     Determine the probability value (1 Marks)
(d)     Provide an interpretation of the P-value (1 Mark)

Note: if you need to use symbols , please use

• "u" for population mean "μ", 

• Ho and Ha for  for the null and alternate hypothesis,

• "Y-hat" for "ŷ", "alpha" for α
  
  

Please provide your answers to the above questions by typing your answers using simple text. You need not show the work in detail.

Question 31

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Long answer question  [7 marks]

The university would like to conduct a study to estimate the true proportion of all university students who have student loans. According to the study, in a random sample of 215 university students, 86 have student loans.

(a) Construct a 99% confidence interval for estimating the true proportion of all university students who have student loans (2 marks)

 (b) Provide an interpretation of the confidence interval in part (a). (1mark)

 (c) Conduct an appropriate hypothesis test, at the 1% level of significance to test the claim that more than 30% of all university students have student loans.

1. Provide the hypothesis statement  (1 Marks)

2. Calculate the test statistic value (2 Marks)

3. Determine the probability value (1 Marks)

 
Note: if you need to use symbols , please use

• "u" for population mean "μ", 

• Ho and Ha for  for the null and alternate hypothesis,

• "Y-hat" for "ŷ", "alpha" for α

Please provide your answers to the above questions by typing your answers using simple text. You need not show the work in detail.