The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expe
ID: 3223233 • Letter: T
Question
The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed 33 lb of cheese in 2010. Suppose that you want to decide whether last year's mean cheese consumption is greater than the 2010 mean. a. Identify the null hypothesis. b. Identify the alternative hypothesis. c. Classify the hypothesis test as two tailed, left tailed, or right tailed. d. The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans. e. At the 10% significance level, do the data provide sufficient evidence to conclude that last year's mean cheese consumption for all Americans has increased over the 2010 mean? Assume that sigma = 6.9 pounds. Use a z-test. f. Given the conclusion in part (a), if an error has been made, what type must it be? Explain your answer.Explanation / Answer
Given that,
population mean(u)=33
standard deviation, =6.9
sample mean, x =34.8
number (n)=35
null, Ho: =33
alternate, last year mean cheese consumption is greater than 2010, H1: >33
level of significance, = 0.1
from standard normal table,right tailed z /2 =1.282
since our test is right-tailed
reject Ho, if zo > 1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 34.8-33/(6.9/sqrt(35)
zo = 1.54333
| zo | = 1.54333
critical value
the value of |z | at los 10% is 1.282
we got |zo| =1.54333 & | z | = 1.282
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 1.54333 ) = 0.06138
hence value of p0.1 > 0.06138, here we reject Ho
ANSWERS
---------------
null, Ho: =33
alternate, H1: >33
test statistic: 1.54333
critical value: 1.282
decision: reject Ho
p-value: 0.06138
we have evidence that mean cheese consumption is increased
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