10.44: The international Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two-tail test at the 0.05 level, could the residents of this city be said to be significantly different from their counterparts across the nation?


Answer:

σm =σ / √n = 12 / √4 =6
Find P( = 55 )
P( ( - μ ) / σm = ( 55 - 50 ) / 6 )
= P( Z = 0.83)
=0.2967


μ = 1.65 cups
n = 38 people
μ = 1.65 cups
n = 38 people
= 1.84 cups
σ = 0.85 cups

μ = 1.65 cups
n = 38 people
= 1.84 cups
σ = 0.85 cups

Ho : residents of this city be said to be similar to their counterparts across the nation
H1: residents of this city be said to be significantly different from their counterparts across the nation

standard error, σm =σ / √n = 0.85 / √38 = 0.138
( - μ ) / σm = ( 1.84 - 1.65 ) / 0.138)
hence Z = 1.38

critical value of z for two-tail test at the 0.05 level = 1.96
since Z is less than critical z, hence we accept the hypotheses
hence residents of this city be said to be similar to their counterparts across the nation