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 must have an average of 100 grams of palladium per shifter. Palladium is expensive, and the customers allege that IBM is adding 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 alleging that IBM is producing time phase shifters with a mean palladium value of less than 100 grams per shifter. IBM denies the allegation, noting that palladium amounts naturally vary due as a result of random variation in production processes.
n = _________ Determine the sample size n for the data.
x = _________ Determine the sample mean x for the data.
sx = _________ Determine the sample standard deviation sx for the data.
SE = _________ Calculate the standard error of the mean for the data.
df = _________ Calculate the number of degrees of freedom.
tc = _________ Calculate tcritical using a confidence level c of 95%
E = _________ Calculate the margin of error for the mean E.
p(__________ ≤ μ ≤ __________) = 0.95 Calculate the 95% confidence interval for the population mean palladium μ.
Write out the null hypothesis that the population mean μ is 100 grams:
Write out the alternate hypothesis that the population mean μ is NOT 100 grams:
Run a hypothesis test at a risk of a type I error alpha α = 0.05
tc = ____________________ Calculate the value of tcritical
t = ____________________ Calculate the value of the t-statistic t
p-value = ____________________ Use =tdist(abs(t),n−1,2) to calculate the p-value.
____________________ Is the sample mean x significantly different from the population mean μ of 100 grams for an alpha α of 0.05?
_____________________ At an alpha α of 5%, would you fail to reject|or|reject the null hypothesis?
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?