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

Answer:

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

Step-by-step 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

                $t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }$

               $t = \frac{1.84-1.65}{\frac{0.85}{\sqrt{38} } }$

              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.