MS 150 quiz ten 10.2 • Name:

Palladium
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18 November 2009

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.

__________ Calculate the sample size n.
__________ Calculate the sample mean x.
__________ Calculate the sample standard deviation sx.
__________ Is the sample mean x less than 100?
__________ What is the point estimate for the population mean μ based on the sample mean x?
Write out the null hypothesis that the population mean μ is 100 grams: H₀:
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
____________________ Calculate the value of t_critical
____________________ Calculate the value of the t-statistic t
_________________________________ Do we reject or fail to reject the null hypothesis?
____________________ Is the sample mean x statistically significantly different from the population mean μ of 100 grams?
The judge is willing to make a legal judgment based on a risk of a type I error of 5%. Should the judge rule rule in favor of the customers (plaintiffs) against IBM | OR | rule in favor of IBM (defendants) against the customers?

Hypothesis Testing
Statistic or Parameter	Symbol	Equations	OpenOffice
Relationship between confidence level c and alpha α for two-tailed tests		1 − c = α
Calculate t-critical for a two-tailed test	t_c		=TINV(α;df)
Calculate a t-statistic t	t		=(x - μ)/(sx/SQRT(n))
Calculate a two-tailed p-value from a t-statistic	p-value		= TDIST(ABS(t);df;2)