The united States ranks ninth in the world in per capita chocolate consumption;

Question

The united States ranks ninth in the world in per capita chocolate consumption; the aver- age American eats 9.5 pounds of chocolate annually (Forbes, July 22, 2015). Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of The Hershey Company’s corporate headquarters. A sample of 36 individuals from the Hershey area showed a sample mean annual consumption of 10.05 pounds and a standard devi- ation of s 5 1.5 pounds. using a 5 .05, do the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the united States?

Explanation / Answer

Here sample size = n = 36
sample mean = 10.05 pounds, sample sd = 1.5 pounds, population mean = 9.5 pounds

Null hypothesis = Chocolate consumption in Hershey, Pennsylvania is same as average american consumption of 9.5 pounds
Alternative hypothesis = Chocolate consumption in Hershey, Pennsylvania is higher than average american consumption of 9.5 pounds
This is one tailed t test.

Standard error = sd/sqrt(n) = 1.5/sqrt(36) = 0.25
Degrees of freedom = n - 1 = 36 - 1 = 35
t statistic = (10.05 - 9.5)/0.25 = 2.2

Here significance level = 0.05
So critical probability = 1 - 0.05/2 = 0.975
Degrees of freedom = 35

Now Critical value of the test statistic can be found out using the t table, which is 2.03

Since the test statistic value 2.2 is greater than the critical value of 2.03, we reject the null hypothesis. So we can say that Chocolate consumption in Hershey, Pennsylvania is higher than average american consumption of 9.5 pounds.

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