i) Interpret the ensemble of forecasts in each case and include a plot of each.

(ii) Comment on the degree of consensus between the CPC and ECMWF ensemble

forecasts.

(iii) Briefly explain why it is necessary to run an ensemble of forecasts in order to predict

ENSO.

The two graphs are listed below.

http://www.cpc.ncep.noaa.gov/products/people/wwang/cfsv2fcst/CFSv2SST8210.html

https://www.ecmwf.int/en/forecasts/charts/seasonal/seasonal_nino_plumes_public_eurosip?time

=2018010100,0,2018010100&nino_area=3.4

Ms. Fitness-Buff, a high school gym teacher, wants to propose an after-school

fitness program. To get an idea of the fitness level of the students at her school, she takes a random sample of 75 students and records the number of hours the students exercised in the past week. Her sample mean is 2.25 hours and she knows from past research that the population standard deviation is 2 hours. She wants to know if this varies from a population mean of 3 hours/week.


Calculate the probability of making a Type II error if the true population mean is 2.75.

All work must be shown step by step. When using Excel for calculations

list the Excel functions used and when they were used and explain how you arrived at the answers. Attach the Excel file.
Players   Round 1
1.     70
2.     71
3.     70
4.     72
5.     70
6.     67
7.     71
8.     68
9.     67
10. 70
11. 72
12. 72
13. 70
14. 70
15. 68
16. 68
17. 71
18. 70
19. 69
20. 67
Players            Round 2
 
1.     72
2.     72
3.     75
4.     71
5.     69
6.     67
7.     67
8.     75
9.     73
10. 69
11. 72
12. 70
13. 73
14. 77
15. 70
16. 65
17. 70
18. 68
19. 68
20. 71
 
Tallies in the first and fourth (final) rounds for a sample of 20 golfers who competed in the PGA tournaments are listed above. Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean tally for the fourth and final round. You are intrigued: Does the pressure of playing in the final round cause tallies to go up? Or does the increased player concentration cause tallies to come down?


  PLEASE INCLUDE THE EXCEL FORMULAS USED


1.  Use  a = 0.10 to test for a statistically significant difference between the populations means for the first- and fourth-round tallies. What is the p-value? What is your conclusion?
 
2.  Find the point estimate for the difference between the two population means. For which round is the population mean tally lower?
 
3.    Develop a 90% confidence interval estimate for the difference between the population means. Use the single population methodology where the confidence interval is given by 
?¯d±t(?α/2)sd?/√n.?
 Notice that 0 is in this interval: what does this say about the statistical significance of the difference in the means?

A local gym conducts a survey among the people in a mall.Which survey question would have a qualitative response?

• How many servings of fruits do you eat every day? 
• Do you exercise daily?
• How much do you weigh, in pounds?
• What is the amount of weight you can bench press, in pounds?

Let Z cP (Z

be a standard normal random variable. Use the calculator provided, or this table, to determine the value of 

≤ c)=0.2327

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.