sb1 q11 10.3 • Name:

Palladium
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Intergalactic Blackhole Machining corporation produces titanium-palladium time phase shifters used in time warp communication gear. Customers have noted an unusually high rate of misaligned time phasing. The customers have blamed the shifter units. To operate correctly the shifters should have an average of 100 grams of palladium per shifter. Palladium is expensive, and the customers are accusing IBM of putting in too little palladium as a way to cut shifter production costs and make more money. The customers have filed a class action suit in court accusing IBM of having a mean palladium value of less than 100 grams per shifter.

IBM denies the charge, noting that palladium amounts naturally vary due as a result of random variation in production processes.

  1. n = __________ Calculate the sample size n.
  2. x = __________ Calculate the sample mean x.
  3. sx = __________ Calculate the sample standard deviation sx.
  4. SE = __________ Calculate the standard error SE.
  5. __________ Is the sample mean x less than 100?
  6. Write out the null hypothesis that the population mean μ is 100 grams:
    H0:
  7. Write out the alternate hypothesis that the population mean μ is NOT 100 grams:
    H1:

    Run a hypothesis test at a risk of a type I error alpha α = 0.05
  8. tc = ____________________ Calculate the value of tcritical
  9. t = ____________________ Calculate the value of the t-statistic t
  10. p-value = ____________________ Use =tdist(abs(t),n−1,2) to calculate the p-value.
  11. ____________________ Calculate the maximum confidence we can have that the sample mean does not come from a population with a mean value of 100 by calculating 1−p-value.
  12. ____________________ Is the sample mean x statistically significantly different from the population mean μ of 100 grams?
  13. _____________________ At an alpha α of 5%, would you fail to reject |or| reject the null hypothesis?
  14. The judge is willing to make a legal judgment based on a 5% risk of rejecting a true null hypothesis. Should the judge rule in favor of the customers (plaintiffs) against IBM | OR | in favor of IBM (defendants) against the customers?