Question

Test the appropriate hypotheses. Use the p-value method here. Annual per capita consumption of milk is 21.6 gallons. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s=4.8. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City equals to the national mean.

Hint: Notice that n=16<30 hence you need to use the t-table. Hence, locate the probability for one (right) tail. You won't get one single value, but a range of possible values. Then multiply it by two (to take into account the left tail) and compare to 0.05.

a) What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?

b) At α =.05, test for a significant difference. What is your conclusion?

Answer 1

Solution-A:

is a point estimate of the difference between mean annual consumption in Webster City and the national mean

=xbar-mu

=24.1-21.6

=2.5

b) At α =.05, test for a significant difference. What is your conclusion?

Ho:

Ha:

alpha=0.05

test statistic is

t=xbar-mu/s/sqrt(n)

t=(24.1-21.6)/(4.8/sqrt(16))

t= 2.083333

df=n-1=16-1=15

p value for two tail test in excel

=T.DIST.2T( 2.083333,15)

=0.054743

p>alpha

p>0.05

Do not reject Ho

Conclusion:

There is sufficient statistical evidence at 5% level of significance to conlcude that the mean annual consumption in Webster City equals to the national mean.