E270 HW 6

RSaleem
 (Not rated)
 (Not rated)
Chat
Home>Homework Answsers>Mathematics homework help>Numerical analysis homework help
NAME:        
Email:        
Enter your LETTER answers HERE      
 ↓        
1  Note:      
2  When done, using your last name and firstname, save THIS FILE as,  
3  e270Lastname Firstname HW6(No space between E270 and Last name)
4  and e-mail it tostowfig@iupui.edu   
5         
6  Example:      
7  e270Smith Adam HW6YES   
8  e270 Smith Adam HW6NO   
9    
 
  
 
    
10        
11        
12        
13        
14   PAY ATTENTION!  
15     
16         
17         
18         
19         
20         
          
1Which of the following statements about Type I and Type II errors is correct  
aType I:  Reject a true alternative hypothesis.  Type II: Do not reject a false alternative. 
bType I:  Do not reject a false null hypothesis.  Type II: Reject a true null hypothesis. 
cType I:  Reject a false null hypothesis.  Type II: Reject a true null hypothesis.  
dType I:  Reject a true null hypothesis.  Type II: Do not reject a false null hypothesis.  
          
2You are reading a report that contains a hypothesis test you are interested in. The writer of the report writes that the p-value for the test you are interested in is 0.061, but does not tell you the value of the test statistic. From this information you can:
 
 
aNot reject the hypothesis at a Probability of Type I error = 0.05, and not reject at a Probability of Type I error = 0.10
 
bReject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error = 0.10
 
cNot reject the hypothesis at a Probability of Type I error = .05, but reject the hypothesis at a Probability of Type I error = 0.10
 
dReject the hypothesis at a Probability of Type I error = .05, but not reject at a Probability of Type I error = 0.10 
 
          
3The random sample below is obtained to test the following hypothesis about the population mean.
 H₀:  μ  ≤ 120       
 H₁:  μ  >120       
 1522036717722010123214134
 49531772312818110103214
 19899126183701614811869
 18216619959172401772842
 12610415712319976106162135
 1745564126176621359154
 141961641867115018690140
 17718920950262331628135
 16917119811611523617680130
 59227212167356113672123
 22010013517170589228141
 522718113823180115153187
 2352122351671361673166156
 2091281666623476207154188
 210202198141921011136170
 2142312894125214316472
          
 The level of significance of the test is α = 0.05.   Compute the relevant test statistic. 
 This is a(n) _______ (two-tail, upper-tail, lower-tail) test.  The test statistic is TS = _______. 
aUpper tail test.  TS =1.34     
 Do not reject H₀:  μ  ≤ 120.  Conclude that the population mean is not greater than 120. 
bUpper tail test.  TS =1.88     
 Reject H₀:  μ  ≤ 120.  Conclude that the population mean is greater than 120.  
cUpper tail test.  TS =1.88     
 Reject H₀:  μ  ≤ 120.  Conclude that the population mean is greater than 120.  
dLower tail test.TS =1.88     
 Do not reject H₀:  μ  ≤ 120.  Conclude that the population mean is less than 120.  
          
4Consider the following hypothesis test.     
 H₀:  μ  ≥15       
 H₁:  μ  <15       
 A random sample of n = 15 yielded the following observations   
 8711118    
 13812135    
 2121191518    
 Use α =0.05       
 TS = ______CV = ______State the decision rule.    
a-1.743-1.761Do not reject H₀.  Conclude the mean is not less than 15.  
b-1.74-1.64Reject H₀.  Conclude the mean is less than 15.  
c1.8472.145Do not reject H₀.  Conclude the mean is not less than 15.  
d1.8471.761Reject H₀.  Conclude the mean is less than 15.  
          
5In a recent study, a major fast food restaurant had a mean service time of 164 seconds.  The company embarks on a quality improvement effort to reduce the service time and has developed improvements to the service process.  The new process will be tested in a sample of stores.  The new process will be adopted in all of its stores, if it resulted in decreased service time.  To perform the hypothesis test in the previous question, the sample of 54 stores yields the following data (seconds).
 
 
 
 
          
 157115115115134174128136161
 127139125145199161182144199
 156117129193173146128166185
 147136180184116172116193183
 184160120161161122191170124
 130191170190194139114195183
          
 Use α =0.05       
 |TS| = ______|CV| = ______      
a2.3351.674Do not reject H₀.  The mean is not less than 164 seconds.  Do not adopt the new process.
   
b2.3351.674Reject H₀.  The mean is less than 164 seconds.  Adopt the new process.
c1.6741.349Reject H₀.  The mean is less than 164 seconds.  Adopt the new process.
d1.3491.674Do not reject H₀.  The mean is not less than 164 seconds.  Do not adopt the new process.
   
          
6According to Kelley Blue Book, the mean price for one-to three-year-old used cars nationwide is $23,400.  to compare the average price of similar used cars in central indiana, a random sample of 120 such cars were selected.  The sample mean was $21,824 with a standard deviation of 7,309.  Does the sample provide significant evidence that the mean price of one-to-three-year old used cars is different from the national mean price?
 
 
 
 
 Use α =0.05       
ap-value =0.044Reject H₀.  Conclude that the dealership's price is different from the national mean price.
   
bp-value =0.124Do not reject H₀.  Conclude that the dealership's price is not different from the national mean price.
   
cp-value =0.0091Do not reject H₀.  Conclude that the dealership's price is not different from the national mean price.
   
dp-value =0.0182Reject H₀.  Conclude that the dealership's price is different from the national mean price.
   
          
7The 2009 mean annual salary of business degree graduates in accounting was $47,900.  In a follow-up study in June 2011, a sample of n = 120 graduating accounting majors yielded a sample mean of $49,500 and standard deviation of $8,200.  Does the 2011 study provide a significant proof that the mean salary in 2011 is higher than in 2009?  Perform this test of hypothesis at a 5% level of significance.
 
 
 
ap-value =0.0524Do not reject H₀.  Conclude that the mean annual salary in 2011 is no greater than in 2009.
   
bp-value =0.0524Reject H₀.  Conclude that the mean annual salary in 2011 is greater than in 2009.
cp-value =0.0162Reject H₀.  Conclude that the mean annual salary in 2011 is greater than in 2009.
dp-value =0.0162Do not reject H₀.  Conclude that the mean annual salary in 2011 is no greater than in 2009.
   
          
8A production line operates with a mean filling weight of 16 ounces per container.  Overfilling or under filling is a serious problem, and the production line should be shut down if either occurs.  A quality control inspector samples 20 items every 2 hours and at that time makes the decision of whether to shut the line down for adjustment.  On sample provides the following data:
 
 
 
  15.816.116.216.116.1   
  16.616.316.315.916.1   
  16.215.81616.315.9   
  1615.916.115.916.2   
 α =0.05       
 Decision Rule:  Reject H₀ if TS > CV     
 TS = ______CV = ______       
a2.0002.093Do not reject H₀.  Do  not shut the line down for adjustment. 
b2.0001.96Reject H₀.  Shut the line down for adjustment.  
c1.7861.729Reject H₀.  Shut the line down for adjustment.  
d2.041.64Do not reject H₀.  Shut the line down for adjustment.  
          
9The mean cholesterol level in women ages 21-40 in the United States is 190 mg/dl.  A study is conducted to determine the cholesterol levels among recent female Asian immigrants.  The following is the cholesterol level of a random sample of 108 recent female Asian immigrants.
 
 
 239105251216220120218195129
 125196193108178187111176178
 141190214180172204118108124
 238248253208135146122209254
 209232238251110224249219219
 124226252189212163205202190
 195116125250244140237192191
 224105201194136245118150165
 132171245166218159130255131
 185210223153167174239200107
 235123224221106212212130154
 200140170202247112153150205
 Does the sample provide significant evidence that mean cholesterol level of recent female Asian immigrants is lower than the mean cholesterol level among all females in the United States?  State the null and alternative hypotheses.  Compute the test statistic and the p-value.  State the decision rule.
 
 
 Round x̅ to two decimal points and the standard error to three decimal points.  
 p-value = ______       
a0.069The evidence is significant at α = 0.05, but not significant at α = 0.01. 
b0.069The evidence is significant at α = 0.10, but not significant at α = 0.05. 
c0.034The evidence is significant at α = 0.05, but not significant at α = 0.01. 
d0.034The evidence is significant at α = 0.01, but not significant at α = 0.05. 
          
10We want to test the hypothesis that mothers with low socio-economic status (SES) deliver babies whose birth weights are lower than "normal".  To test this hypothesis, a list is obtained of birth weights from 100 consecutive, full-term, live-born deliveries from the maternity ward of a hospital in a low-SES area.  The mean birth weight is x̅ = 115 oz. with a standard deviation s = 24 oz.  Nationwide, the mean birth weight in the United States is 120 oz.  At α = 0.05, does this sample provide significant evidence that the mean birth weight of babies born to mother with low SES is lower than "normal"?
 
 
 
 
 
ap-value =0.0188Reject H₀ at the 5 percent level of significance.  Conclude that the mean birth weight of babies born to low-SES mothers is lower than "normal".
   
bp-value =0.0188Reject H₀ at the 1 percent level of significance.  Conclude that the mean birth weight of babies born to low-SES mothers is lower than "normal".
   
cp-value =0.0785Do not reject H₀ at the 5 percent level of significance.  Conclude that the mean birth weight of babies born to low-SES mothers is no lower than "normal".
   
dp-value =0.0785Do not reject H₀ at the 10 percent level of significance.  Conclude that the mean birth weight of babies born to low-SES mothers is no lower than "normal".
   
          
11At Western University the historical mean scholarship examination score of entering students has been 900.  Each year a sample of applications is taken to see whether the examination scores are at the same level as in previous years.  The null hypothesis tested is H₀: μ = 900.  A sample of n = 81 students in this year’s class provided a sample mean score of x̅ = 935 and a standard deviation of s = 180. 
 
 
 
 First build a 95% confidence interval for the population mean score.   
aThe confidence interval captures µ₀ = 900.  Do not reject H₀.  Conclude that the current mean score is not different from the historical mean score.
 
bCompared to the MOE, x̅ − µ₀ is within the margin of error.  Conclude that the current mean score is not different from the historical mean score.
 
cCompared to the MOE, x̅ − µ₀ is outside the margin of error.  Conclude that the current mean score is different from the historical mean score.
 
dBoth a and b are correct.      
          
12Consider the following hypothesis test.     
  H₀:  π  ≤0.5H₁:  π  >0.5    
 A sample of n = 200 provided a sample proportion of p̅ = 0.57.  At α = 0.05, what is your conclusion?
 TS = ______CV = ______State the decision rule.    
a1.981.64Conclude the population proportion is no greater than 0.50. 
b1.981.64Conclude the population proportion is greater than 0.50. 
c2.981.96Conclude the population proportion is no greater than 0.50. 
d2.981.96Conclude the population proportion is greater than 0.50. 
          
13In the previous question, the prob value for the test is:    
a0.0239        
b0.0427        
c0.0618        
d0.0808        
          
Next THREE questions are based on the following    
Consider the following hypothesis test.      
   H₀:  π ≥ 0.75     
   H₁:  π < 0.75     
Compute the test statistic and the p-value for the following three cases.   
14n =200p̅ =0.70α =0.05   
ap-value =0.0258Conclude that the population proportion is not less than 0.75. 
bp-value =0.0258Conclude that the population proportion is less than 0.75. 
cp-value =0.0516Conclude that the population proportion is not less than 0.75. 
dp-value =0.0516Conclude that the population proportion is less than 0.75. 
          
15n =200p̅ =0.70α =0.10   
ap-value =0.0516Conclude that the population proportion is less than 0.75. 
bp-value =0.0516Conclude that the population proportion is not less than 0.75. 
cp-value =0.0258Conclude that the population proportion is less than 0.75. 
dp-value =0.0258Conclude that the population proportion is not less than 0.75. 
          
16n =900p̅ =0.72     
ap-value =0.0188Reject H₀ at α = 0.10, but do not reject at α = 0.05.  
bp-value =0.0188Reject H₀ at α = 0.05, but do not reject at α = 0.01.  
cp-value =0.0672Reject H₀ at α = 0.10, but do not reject at α = 0.05.  
dp-value =0.0672Reject H₀ at α = 0.05, but do not reject at α = 0.10.  
          
17The Center for Workforce Development found that 40% of Internet users received more than 15 e-mail messages per day in 2008.  In 2012, a similar study on the use of e-mail was repeated.  The purpose of the study was see whether use of e-mail has increased.  Formulate the null and alternative hypotheses to determine whether an increase has occurred in the proportion of Internet users receiving more than 10 e-mail messages per day.
 
 
 
 
 To test the hypothesis at a 5% level of significance, a sample of 420 Internet users found 189 receiving more than 10 e-mail messages per day.  Compute the test statistic and the p-value.
 
 p-value = ______.       
a0.0183Reject H₀ at α = 0.10.  Conclude the population proportion is greater than 0.40. 
b0.0183Reject H₀ at α = 0.05.  Conclude the population proportion is greater than 0.40. 
c0.0544Do not reject H₀ at α = 0.05.  Conclude the population proportion is not greater than 0.40.
dBoth a and b are correct.      
          
18We want to test the hypothesis that at least 75% of drivers on a freeway violate the speed limit.  In a random sample of n = 900 vehicles, 657 violated the speed limit.  Compute the sample proportion.
 
 State the null and alternative hypotheses and the decision rule.   
aReject H₀ at α = 10% and conclude less than 75% of drivers violate the speed limit.  But, do not reject H₀ at α = 5% and conclude 75% or more of drivers violate the speed limit.
 
bReject H₀ at α = 5%.  Conclude less than 75% of drivers violate the speed limit.  
cReject H₀ at α = 5%.  Conclude more than 75% of drivers violate the speed limit. 
dReject H₀ at α = 1%.  Conclude less than 75% of drivers violate the speed limit.  
          
19At least 20% of all workers are believed to be willing to work fewer hours for less pay to obtain more time for personal and leisure activities.  A recent poll consisting of 600 respondents found 17% willing to work fewer hours for less pay to obtain more personal and leisure time.  At 5% level of significance, does the sample result support the claim that at least 20% of all workers are willing to work fewer hours for less pay to obtain more time for personal and leisure activities? Round the proportion to two decimal point.
 
 
 
 
 
a1.641.84Do not reject H₀.  Conclude that no less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
   
b1.841.96Do not reject H₀.  Conclude that no less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
   
c1.841.64Reject H₀.  Conclude that less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
   
d1.561.64Do not reject H₀.  Conclude that no less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
   
          
20In the previous question, the p-value is _______.    
a0.0594        
b0.0329        
c0.0233        
d0.0158        
    • 11 years ago
    Report issue
    Perfect Solution
    NOT RATED

    Purchase the answer to view it

    • e270hw6-1_1.xlsx