MATHEMATICS

1) A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 6. The sample mean is 23. (Round your answers to 3 decimal places.)

 

A) The standard error of the mean is ________

 

B) The 99 percent confidence interval for the population mean is between _______and ________

2) The owner of Britten’s Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2.63 eggs per month (Round your answer to 3 decimal places.)

A) What is the best estimate of this value?

B) For a 99 percent confidence interval, the value of t   is ______

C) The 99 percent confidence interval for the population mean is _______to ________

3) As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 230 applicants 26 failed the test.

A)  Develop a 90 percent confidence interval for the proportion of applicants that fail the test.  (Round your  answers to 3 decimal places.)

For the applicants the confidence interval is between _______ and _______

B) Would it be reasonable to conclude that more than 11 percent of the applicants are now failing the test? Yes or No

C) In addition to the testing of applicants, Fashion Industries randomly tests its employees throughout the year. Last year in the 520 random tests conducted, 22 employees failed the test. Would it be reasonable to conclude that less than 6 percent of the employees are not able to pass the random drug test? Yes or No

4) A sample of 48 observations is selected from a normal population. The sample mean is 22, and the population standard deviation is 6.
Conduct the following test of hypothesis using the .05 significance level.
H0 : μ ≤ 21
H1 : μ > 21

 

A)  Is this a one- or two-tailed test?
 
   

 

B) What is the decision rule? (Round your answer to 2 decimal places.)
   
   H0 and H1 when z >
C) What is the value of the test statistic? (Round your answer to 2 decimal places.)

 

  Value of the test statistic  

 

D) What is your decision regarding H0?
   
   
     There is  evidence to conclude that the population mean is greater than 21.

 

E) What is the p-value? (Round your answer to 4 decimal places.)
   
   
5) Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less to handle than paper ticketing. However, in recent times the airlines have received complaints from passengers regarding their e-tickets, particularly when connecting flights and a change of airlines were involved. To investigate the problem an independent watchdog agency contacted a random sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March. The information is reported below.
 14 14 16 12 12 14 13 16 15 14 12 15 15 14 13 13 12 13 10 13
At the .05 significance level can the watchdog agency conclude the mean number of complaints per airport is less than 15 per month? Conduct a test of hypothesis and interpret the results.
PictureClick here for the Excel Data File
(a) What assumption is necessary before conducting a test of hypothesis?

 

(b) What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
   
  Reject H0 : μ ≥ 15   and accept H1 : μ < 15   when the test statistic is  .
   
  The value of the test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
(c) What is your decision regarding H0 ?

 

6)

The liquid chlorine added to swimming pools to combat algae has a relatively short shelf life before it loses its effectiveness. Records indicate that the mean shelf life of a 5-gallon jug of chlorine is 2,160 hours (90 days). As an experiment, Holdlonger was added to the chlorine to find whether it would increase the shelf life. A sample of nine jugs of chlorine had these shelf lives (in hours):
2,159 2,170 2,180 2,179 2,160 2,167 2,171 2,181 2,185
At the .025 level, has Holdlonger increased the shelf life of the chlorine?
Picture  Click here for the Excel Data File
A) What is the decision rule? (Round your answer to 3 decimal places.)
   
  Reject  H0 : μ ≤ 2,160 and accept  H1 : μ > 2,160 when the test statistic is .
B) The value of the test statistic is . (Round your answer to 2 decimal places.)
C) What is your decision regarding H0  ?

 

D) The p-value is

7)

The following hypotheses are given.
H0 : π ≤ 0.82
H1 : π > 0.82

 

A sample of 100 observations revealed that p=0.93. At the 0.02 significance level, can the null hypothesis be rejected?
A)  State the decision rule. (Round your answer to 2 decimal places.)
   
    H0 and H1 if z >

 

B)  Compute the value of the test statistic. (Round your answer to 2 decimal places.)

 

  Value of the test statistic  

 

C)  What is your decision regarding the null hypothesis?
    H0.
8) Tina Dennis is the comptroller for Meek Industries. She believes that the current cashflow problem at Meek is due to the slow collection of accounts receivable. She believes that more than 60 percent of the accounts are in arrears more than three months. A random sample of 200 accounts showed that 140 were more than three months old. At the .01 significance level, can she conclude that more than 60 percent of the accounts are in arrears for more than three months?

 

A) State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)
  H0: π ≤  
  H1: π >  

 

B) State the decision rule for .01 significance level. (Round your answer to 2 decimal places.)
  Reject H0 if z is >  

 

C) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
  z value is  

 

D) At the .01 significance level, can she conclude that more than 60 percent of the accounts are in arrears for more than three months?
   H0. Ms. Dennis is in concluding that more than 60% of the   accounts are more than 3 months old.
9) The cost of weddings in the United States has skyrocketed in recent years. As a result many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $10,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the .005 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?
9.5 9.1 10.8 9.7 8.5 9.4 8.6 9.4
A) State the null hypothesis and the alternate hypothesis. Use a .005 level of significance. (Enter your answers in thousands of dollars.)

 

  H0: μ ≥  
  H1: μ <  
B) State the decision rule for .005 significance level. (Round your answer to 3 decimal places.)

 

  Reject H0 if t <  
C) Compute the value of the test statistic. (Round your answer to 3 decimal places.)

 

  Value of the test statistic  
D) At the .005 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?

 

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