Question

QUESTION 1

1. Assume that the two samples of five cereal boxes (one sample for each of two cereal varieties) listed on the TCCACCTC Web site were collected randomly by organization members. For each sample, assume that the population distribution of individual weight is normally distributed, the average weight is indeed 368 grams and the standard deviation of the process is 15 grams, and obtain the following using Excel and PHStat:

   Weights of Oxford O’s boxes
   360.4
   361.8
   362.3
   364.2
   371.4
   
   Weights of Alpine Frosted Flakes with Vitamins & Minerals boxes
   366.1
   367.2
   365.6
   367.8
   373.5 All answers should be accurate to 2 decimal places.

2. (a) For the Oxford's O:

      (i) The value of the sample mean =

      (ii) The proportion of all samples for each process that would have a sample mean less than the value you calculated in step (a)(i) =

      (iii) The proportion of all the individual boxes of cereal that would have a weight less than the value you calculated in step (a)(i) =

      (iv) The probability that an individual box of cereal will weigh less than 368 grams =

      (v) The probability that 4 out of the 5 boxes sampled will weigh less than 368 grams =

      (vi) The lower limit of the 95% confidence interval for the population average weight =

      (vii) The upper limit of the 95% confidence interval for the population average weight =

   (b) For the Alpine Frosted Flakes:

      (i) The value of the sample mean =

      (ii) The proportion of all samples for each process that would have a sample mean less than the value you calculated in step (b)(i) =

      (iii) The proportion of all the individual boxes of cereal that would have a weight less than the value you calculated in step (b)(i) =

      (iv) The probability that an individual box of cereal will weigh less than 368 grams =

      (v) The probability that 4 out of the 5 boxes sampled will weigh less than 368 grams =

      (vi) The lower limit of the 95% confidence interval for the population average weight =

      (vii) The upper limit of the 95% confidence interval for the population average weight =

QUESTION 2

1. Oxford Cereals then conducted a public experiment in which it claimed it had successfully debunked the statements of groups such as the TriCities Consumers Concerned About Cereal Companies That Cheat (TCCACCTC) that claimed that Oxford Cereals was cheating consumers by packaging cereals at less than labeled weights. Review the Oxford Cereals' press release and supporting documents that describe the experiment at the company's Web site and then answer the following assuming that now you have no information about the mean and standard deviation of the population distribution of the weight of all boxes of the cereal produced:

   Weight
   351.8
   360.65
   372.74
   382.96
   375.28
   352.16
   374.15
   361.8
   366.67
   398.86
   384.34
   367.53
   361.59
   364.47
   382.93
   366.88
   368.14
   408.19
   356.03
   379.27
   380.38
   386.44
   378.72
   342.05
   380.29
   361.1
   355.11
   387
   346.86
   391.94
   366.3
   350.52
   397.27
   349
   373.78
   384.04
   392.55
   361.98
   377.07
   390.88
   395.86
   370.21
   380.66
   389.33
   361.15
   386.74
   353
   354.22
   374.24
   363.77
   352.08
   364.11
   359.79
   367.12
   375.84
   343.29
   357.7
   384.75
   380.72
   356.22
   389.72
   375.28
   380.44
   379.14
   364.64
   379.63
   369.29
   337.1
   371.42
   347.63
   363.86
   381.28
   379.21
   366.26
   365.15
   351.33
   375.91
   363.32
   357.96
   375.58

   All answers should be accurate to 2 decimal places.

   (a) For a two-tailed t-test on whether the population mean weight is equal to 368g:

      (i) The value of the t-test statistic is =

      (ii) The p-value of the t-test statistic is =

      (iii) The lower-critical value is =

      (iv) The upper-critical value is =

   (b) For an upper-tailed t-test on whether the population mean weight is more than 368g:

      (i) The value of the t-test statistic is =

      (ii) The p-value of the t-test statistic is =

      (iii) The upper-critical value is =

   (c) For the 95% confidence interval for the population average weight:

      (i) The lower limit =

      (ii) The upper limit =

Answer 1

(vi) The lower limit of the 95% confidence interval for the population average weight =350.87

Excel commend: "=ROUND(364.02-NORM.INV(0.975,0,1)*15/SQRT(5),2)"

   (vii) The upper limit of the 95% confidence interval for the population average weight =377.17

Excel commend: "=ROUND(364.02+NORM.INV(0.975,0,1)*15/SQRT(5),2)"