Question 406752
  <pre><font size = 3 color = "indigo"><b>
Hi
Understand completely, recall there was a time I was self taught on most
ALL early math at any rate:  (country school:)
Might recommend checking out the statistic's section on this site: 
great learning tool selecting previous questions answered, of interest to You.
2. Given a level of confidence of 95% and a population standard deviation of 6, answer the following:
(A) What other information is necessary to find the sample size (n)?
   confidence interval or 'margin of error'
(B) Find the Maximum Error of Estimate (E) if n = 84. Show all work. 
            ME = 1.96[6/sqrt(84)] 

3. A sample of 134 golfers showed that their average score on a particular golf course was 93.23 
with a standard deviation of 6.25. 
Answer each of the following (show all work
and state the final answer to at least two decimal places.): 
(A) Find the 98% confidence interval of the mean score for all 134 golfers. 
ME = 2.3263[6.25/sqrt(134)] 
CI: 93.23- ME < u < 93.23 + ME			

(B) Find the 98% confidence interval of the mean score for all golfers if this is a sample of 110 golfers 
instead of a sample of 134.
ME = 2.3263[6.25/sqrt(110)] 
CI: 93.23- ME < u < 93.23 + ME	
(C) Which confidence interval is larger and why? (Points : 6) 
Note: the Larger the sample size, the smaller ME is and therefore the
confidence interval is larger with the smaller sample size.

5. The diameters of grapefruits in a certain orchard are normally distributed
 with a mean of 5.91 inches and a standard deviation of 0.52 inches. Show all work. 
(A) What percentage of the grapefruits in this orchard is larger than 5.86 inches? 
   z = 5.86-5.91 /.52 = -.05/.52 = -.0962 
    P(z > -.0962) = 1 - .4617 = .5383  53.83%
(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated.
 What is the probability that the sample mean is greater than 5.86 inches? 
      z = -.05/ .52/sqrt(100) = -.05 /.052 = .9615             
    P(z > -.9615) = 1 -.16815 = .83185   83.185%

Folowing is a summary of Levels of Confidence & their critical regions
	a	a/2	crtical regions	
90%	10	5%	z <-1.645	z >+1.645
95%	5	2.50%	z <-1.96	z >+1.96
98%	2	1%	z <-2.33	z >+2.33
99%	1	0.50%	z<-2.575	z >+2.575