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Has the consumption of red meat decreased over the last 10 years? A researcher selected hospital...

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Statistics

Has the consumption of red meat decreased over the last 10years? A researcher selected hospital nutrition records for 400subjects surveyed 10 years ago and compared the average amount ofbeef consumed per year to amounts consumed by an equal number ofsubjects interviewed this year. The data are given in thetable.
Ten Years Ago This Year
Sample Mean 71 64
Sample Standard Deviation 20 26

(a) Find the test statistic and the p-value. (Round your teststatistic to two decimal places and your p-value to four decimalplaces.)

z =

p-value =

(b) Find a 99% lower confidence bound for the difference (tenyears ago − this year) in the average per-capita beef consumptionsfor the two groups. (Round your answer to two decimal places.)

Answer & Explanation Solved by verified expert
3.6 Ratings (492 Votes)

10 year ago this year
x1            = 71.00 x2            = 64.00
n1           = 400 n2           = 400
σ1           = 20.00 σ2           = 26.00

a)

std error σx1-x2=√(σ21/n1+σ22/n2)    = 1.640
test stat z =(x1-x2-Δo)/σx1-x2     =(71-64)/1.640 = 4.27

p value =0.0000

b)

Point estimate of differnce '=x1-x2 = 7.000
for 99 % CI value of z= 2.576
margin of error E=z*std error = 4.225
lower bound=(x1-x2)-E = 2.78
Upper bound=(x1-x2)+E = 11.22
from above 99% confidence interval for population mean =(2.78 ,11.22)

(please try 2.77 ,11.23 if this comes wrong)
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