Average Breeding Stage

Question

Pig farmers in Shaktoolik, Alaska are  trying  to sell pork  as the “other white meat  besides chicken”  (according to the Shaktoolik  News), claiming  to evolved a leaner more efficient breed of pig. One of the claimed advantages of this new breed of pig is that  it  takes  substantially less time for  a  pig to  reach  the  final  market weight (thus saving the farmer money in feeding and tending).  Based on a national standard the average pig usually takes 160 days of breeding  time with a standard deviation of 40 days.  The agricultural researchers from the University  of the North randomly selected 81 new breed pigs and determined their average breeding days to be 170 days.  At a  twenty  significance  level test the  claim  that  the  new breed  of Shaktoolik  pigs have  the  same  breeding  time .  Assume  the  population  standard deviation is known.

1. Nordstrom  is a leading  retailer  of woman’s clothing is planning  to open a new store  in Scammon  Bay, Alaska.  To  minimize  its start  up  cost Nordstrom not to stock suits for  the tallest 10 percent  and  the shortest  20%  of the woman.  Find the minimum  and  maximum  heights  of  the  woman  suits  to  be  stocked.  Woman normally distributed heights with a mean of 56 inches and a standard deviation  of

17 inches.

Question

1 . In Alaska, a random  sample of 15 eight-grade  students  has a mean score of 265 with a sample standard deviation of 55 on a national  mathematical assessment test. This prompts  a state  school administrator to declare  that  the mean score is more than 260.  At a five percent  significance level, is there  enough evidence to support the administrator’s claim? Assume the population  standard deviation is unknown; use the “t” procedure. (6 points)

2 . In  a  simple  random  sample  of  42 Alaskan  civil engineering  firms  the  mean number  of employees is sixteen.  The population standard deviation is estimated  to be four  employees.  Establish  the  95.5%  confidence  interval  for  the  population mean.  Assume the population  standard deviation is known;  use the “z” procedure. (5 points)

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