5. The price of coffee has been steadily declining since October 2012. The International Coffee Organization (ICO) reported that the mean price for coffee in May 2013 was 126.96 U.S. cents/lb. A random sample of 34 days was obtained and the composite indicator for Brazilian Natural coffee was recorded for each. The sample mean was
x = 130.29 U.S. cents/lb.
Assume the population standard deviation is 8.6 U.S. cents/lb. Is there any evidence to suggest that the mean composite indicator for Brazilian Natural is greater than 126.96? Use
α = 0.05.
a) Give the value of the appropriate zα or zα/2. (Round your answer to four decimal places.)
b) Calculate the test statistic. (Round your answer to four decimal places.)
z =
a)
H0:
<= 126.96
Ha:
> 126.96
This is one (right ) tailed test.
Z
= 1.6449
b)
Test statistics z = (
-
) / (
/ sqrt(n) )
= (130.29 - 126.96) / (8.6 / sqrt(34)
= 2.2578
Since test statistics falls in rejection region (That is greater than 1.6449) , Reject H0.
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