The USDA collects and distributes a wide variety of data about agriculture in the United States. One statistic reported each year is the number of milk cows (in thousands) in each state. A random sample of 10 states is selected, with the number of milk cows reported in both 2011 and 2015.
State 2011 2015 Difference
North Dakota 19 16 -3
California 1769 1778 9
Nevada 29 29 0
Ohio 268 267 -1
New Hampshire 14 14 0
Colorado 128 146 18
Minnesota 468 460 -8
Oklahoma 53 39 -14
Utah 93 96 3
Washington 260 277 17
mean 310.1 312.2 2.1
sd 532.857 535.367 10.159
An agricultural researcher wants to conduct a paired difference test to determine if the mean number of milk cows (in thousands) in the US changed between 2011 and 2015.
Round all calculated values to 4 decimal places as appropriate.
1. Which hypotheses should be used to conduct the test?
A. H0:μdiff=0 vs. Ha:μdiff≠0
B. H0:μdiff<2.1 vs. Ha:μdiff>2.1
C. H0:μdiff=0 vs. Ha:μdiff<0
D. H0:μdiff=0 vs. Ha:μdiff>0
2. Assume the conditions for the hypothesis test are met and find the test statistic and the p-value.
test statistic =
p-value =
3. Based on the p value we have
?
evidence that the null model is not a good fit for our observed data.
4. Construct a 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015.
