Question

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 1

The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance

the null hypothesis is accepted

There is no significant difference between their counterparts across the nation

Explanation:

Step(i):-

Given that the mean of the U.S residents = 1.65

Given that the size of the sample 'n' = 38

Mean of the sample = 1.84

Given that the standard deviation of the sample (S) = 0.85

Step(ii):-

Null hypothesis:H₀:

There is no significant difference between their counterparts across the nation

Alternative Hypothesis:-H₁:

There is a significant difference between their counterparts across the nation

Test statistic

`t = (x^(-) -mean)/((S)/(√(n) ) )`

`t = (1.84-1.65)/((0.85)/(√(38) ) )`

t = 1.3788

Degrees of freedom

ν = n-1 = 38-1 = 37

t₀.₀₅ ,₃₇ = 2.0262

The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance

Null hypothesis is accepted

Final answer:-

There is no significant difference between their counterparts across the nation.