Question

a). Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone.

x	1004	975	992	935	973	934
y	40	100	65	145	79	149

What is the value of the sample test statistic? (Round your answer to two decimal places.)
__________?

b). The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.36 A, with a sample standard deviation of s = 0.46 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

What is the value of the sample test statistic? (Round your answer to three decimal places.) ___________?

Answer 1

a)

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ≠		0

correlation r='Sxy/(√Sxx*Syy) =		-0.9833
test stat t=	r*(√(n-2)/(1-r2))=	-10.81

b)

population mean μ=		0.8
sample mean 'x̄=		1.360
sample size    n=		9
std deviation s=		0.460
std error ='sx=s/√n=0.46/√9=		0.1533
t statistic ='(x̄-μ)/sx=(1.36-0.8)/0.153=		3.652