Question

1. A health professional wishes to estimate the true mean yearly soda consumption (in gallons) of U.S. adults. A sample of 35 adults was taken, and it was found that they consumed an average of 45.6 gallons of soda in one year. The standard deviation of the population is 3.5 gallons We would like to construct a 95% confidence interval estimate for the true mean.
   1. What critical value will you use for a 95% confidence interval? Give the value and specify whether it comes from the standard normal distribution or the t distribution ( or ).

_______________

2. Calculate the margin of error, E. (You must show setup to receive credit. You may round to three decimal places, if needed.)

E = _______________

3. Construct the 95% confidence interval for the population mean yearly soda consumption. (Round limits to one decimal place.)

_______________<  < _______________

Answer 1

Solution :

Given that,

a) Z/2 = Z0.025 = 1.96

b) Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 3.5 /  35)

= 1.160

c) At 95% confidence interval estimate of the population mean is,

- E < < + E

45.6 - 1.160 <   < 45.6 + 1.160

44.4 <   < 46.8