Project #10898 - statistics help

I have about 10 problems I need help with 

1.As a manufacturer of gold, equipment, the Spalding Corporation wants to estimate the proportion of golfers who are left-handed.  (The company can use this information in planning for the number of right-handed and left-handed sets of gold clubs to make).  How many golfers must be surveyed if we want 99% confidence that the sample proportion has a margin of error of 0.25? 

a)  Assume that the proportion found from a previous study suggests that 15% of the golfers are left-handed (based on a USA Today report).  


b)  Assume that there is no available information that could be used as an estimate of the proportion. 


2. A cheese processing company wants to estimate the mean cholesterol content of one-ounce servings of cheese.  The estimate must be within 0.5 milligram of the population mean.  Assuming that the standard deviation is 2.8 milligrams, which confidence level (95% or 99%) requires a larger sample size? 

PART B:  For problems 11-16  perform each of the following steps in order to receive full credit. (10 pts each). 

a) State the hypotheses and identify the nature of the test (left-tailed, two-tailed, etc).   

b)  Traditional method:  Identify the significance level, the appropriate test (Z-test, T-test, 

     1-Prop Z test, etc) and find the critical value(s).  For the P-value method, give the significance level.  

c)  Compute the test value (if using the Traditional method).  For the P-value method, give the 

     z value and the p-value.   

d)  Make the decision to reject OR Do Not reject the null hypotheses.

e)  Make the conclusion in the context of the problem.    


11. Vending Machines, Coffee:  A machine in the student lounge dispenses coffee.  The average cup of coffee is supposed to contain 7.0 ounces.  Eight cups of coffee from this machine show that the average content to be 7.3 ounces with a standard deviation of 0.5 ounce.  Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is more than 7 ounces?  Use a 5% level of significance.      

A)  Ho:  _______________  In words: ________________________________________________________                                                      


      H1:  _______________ In words: _________________________________________________________                                             


B)  Critical Value                                                                          C)  Test Value 





D)  Decision                                                                                  E)   Conclusion











12. Red Blood Cell (RBC) Volume:  Total blood volume (in ml) per body weight (kg) is important in medical research.  For all healthy adults, the RBC volume is about 28 ml/kg.  (Reference: Laboratory and Diagnostic Tests, F. Fischbach).  RBC volume that is too low or too high can indicate a medical problem.  Suppose that a patient has had seven blood tests and the RBC volumes were:  32   25   41   35   30   37   29.  

Assume that the variable x (patient’s RBC volume) has a normal distribution with  EMBED Equation.3   ml/kg.  Use a 1% significance level and determine whether the sample data indicate that this patient’s RBC volume is different from the RBC of healthy adults. 

A)    Ho:  _____________________                                     D)  Decision                              


        H1:  _____________________ 


B)  Critical Value                                                                      E)  Conclusion                               






C)  Test Value  








13.  Auto insurance companies are beginning to consider raising rates for those who use telephones while driving.  The National Consumers Group claims that the problem isn’t too serious because only 10% of the drivers use telephones.  The insurance industry conducts a study and finds that among 500 randomly selected drivers, 90 use telephones (based on data from Prevention Magazine).  At the 0.01 level of significance test the consumer’s group claim.  


A)  Ho:  _____________________                                                     D)  Decision 


      H1:  _____________________ 



B)  Critical Value                                                                                    E)   Conclusion






C)  Test Value 








14.  The Medassist Pharmaceutical Company wants to test Dozenol, a new cold medicine intended for night use.  Tests for such products often include a “treatment group” of people who use the drug and a “control group” of people who don’t use the drug.  Fifty people with colds are given Dozenol and 100 others are not. The systolic blood pressure is measured for each subject, and the results are given below: 

                     Treatment Group                                   Control Group 

                         EMBED Equation.3                                                   EMBED Equation.3  

 The head of the research claims that Dozenol does not affect blood pressure, that is, the treatment population mean and the control population mean are equal.  At α = 0.01 test the claim.


A)  Ho:  _____________________                                                  D)  Decision 


      H1:  _____________________ 


 B)  Critical Value                                                                                E)   Conclusion



C)  Test Value 




15.  Clinical Trial.  The drug Prevnar is a vaccine meant to prevent certain types of bacterial meningitis.  It is typically administered to infants starting around two months of age.  In randomized double-blind clinical trials of Prevnar, infants were randomly divided into two groups: 

             Group 1 (experimental group): subjects received Prevnar

             Group 2 (control group): subjects received a control vaccine (placebo)

After the fist dose 107 of 710 subjects in the experimental group experienced fever as a side effect. 

After the first does, 67 of 611 subjects in the control group experienced fever as a side effect.  

Test the claim that a higher proportion of subjects in Group 1 experienced fever as a side effect than subjects in Group 2 at the  α = 0.05 significance level using the traditional method. 


A)  Ho:  _____________________                                                     D)  Decision 


      H1:  _____________________ 


B)  Critical Value                                                                                    E)   Conclusion


C)  Test Value 



16.  A special diet is intended to reduce the cholesterol of patients at risk of heart disease. If the diet is effective, the target is to have the average cholesterol of this group be below 200. After six months on the diet, an SRS of 50 patients at risk for heart disease had an average cholesterol of 192 with a standard deviation of 21.  Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of the cholesterol for patients in this group is approximately normal. Use 1% significance level. 


A)  Clearly state the hypotheses in the context of the problem. 

      H0:  _____________    In words: __________________________________________________________

      H1: ______________   In words: __________________________________________________________  


B)  If using the critical region method, find the test statistic or test value (by hand or by the calculator).  

      If you are using the p-value method give the corresponding p-value.  





C) If usingthe critical region method:   Give the critical value and draw the associated rejection region.   

      If using P-value method:  Give the significance level and draw the associated rejection region.    



D)  State your decision whether you reject H0 or do not reject H0 and explain why.  Then state your conclusion using complete sentences and explain how you determined that conclusion.








17.  (6pts):  A recent study of how 670 Americans get to work revealed the following data?                                      

                                             T  y  p  e   of   W o r k e r       

                                        Urban           Rural           Total

Automobile                     400               200              600

Public Transportation     50                 20                70

Total                                  450              220              670

If a worker is selected at random, find the following probabilities.  Write the answer as a fraction (do not reduce). 

a)  The worker is an urban worker?  _____________________


b)  The worker is a rural worker who uses public transportation? ______________


c)  The worker is an urban worker or uses public transportation? _________________________


18.  (10 pts).  The following table gives information on average saturated fat (in grams) consumed per day and cholesterol level (in milligrams per hundred milliliters) of eight men.  

 Fat consumption  55  68  50  34  43  58  77  36Cholesterol level 180 215 195 165 170 204 235 150Questions:  

a)  Draw a scatter plot of the data using the grid to the right.  For the vertical axis start with 150 and then count by 10s.   For the horizontal axis count by 10s.

b)  Describe the relationship between the two variables. 





b)  Compute the correlation coefficient r using the calculator.                                                              

Round to 6 decimal places.  _________________________



c)  Give the equation of the regression line.  Round your numbers to  

six decimal places.




d)  Estimate the cholesterol level of a man whose average daily fat consumption is 60 grams.   






Subject Mathematics
Due By (Pacific Time) 08/16/2013 12:00 pm
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