According to a report published by the USDA 3 years ago, a typical American consumes an average of 31.3 pounds of cheese per year.
A researcher at the USDA would like to determine if the average amount of cheese consumed each year by a typical American has changed since the original report was published. The researcher collected data from a random sample of 38 Americans and found that the mean amount of cheese consumed each year by the sample was 31.18 pounds with a standard deviation of 1.965 pounds.
Using ? = 0.2, test the hypothesis that the mean amount of cheese consumed each year by a typical American is different than 31.3 pounds. Use the p-value method.
State the null and alternative hypothesis for this test.
H0 : ?
H1 : ?
Determine if this test is left-tailed, right-tailed, or two-tailed.
left-tailed
two-tailed
right-tailed
Should the standard normal (z) distribution or Student's (t) distribution be used for this test?
The Student's t distribution should be used
The standard normal (z) distribution should be used
Determine the test statistic for the hypothesis test. Round the solution to four decimal places.
Determine the p-value (range) for the hypothesis test.
p-value < 0.001
0.001 < p-value < 0.01
0.01 < p-value < 0.02
0.02 < p-value < 0.05
0.05 < p-value < 0.10
0.10 < p-value < 0.20
p-value > 0.20
Determine the appropriate conclusion for this hypothesis test.
The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean amount of cheese consumed each year by a typical American is different than 31.3 pounds and thus we conclude that the mean amount of cheese consumed each year by the typical American is likely different than 31.3 pounds.
The sample data provide sufficient evidence to reject the alternative hypothesis that the mean amount of cheese consumed each year by a typical American is different than 31.3 pounds and thus we conclude that the mean amount of cheese consumed each year by the typical American is likely 31.3 pounds.
The sample data do not provide sufficient evidence to reject the null hypothesis that the mean amount of cheese consumed each year by a typical American is 31.3 pounds and thus we conclude that the mean amount of cheese consumed each year by a typical American is likely 31.3 pounds.
The sample data provide sufficient evidence to reject the null hypothesis that the mean amount of cheese consumed each year by a typical American is 31.3 pounds and thus we conclude that the mean amount of cheese consumed each year by a typical American is likely different than 31.3 pounds.
