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:
<u><em>Step(i):-</em></u>
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
<u><em>Step(ii):-</em></u>
<u><em>Null hypothesis:</em></u>H₀:
There is no significant difference between their counterparts across the nation
<u><em>Alternative Hypothesis:-</em></u>H₁:
There is a significant difference between their counterparts across the nation
Test statistic
![t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bx%5E%7B-%7D%20-mean%7D%7B%5Cfrac%7BS%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
![t = \frac{1.84-1.65}{\frac{0.85}{\sqrt{38} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B1.84-1.65%7D%7B%5Cfrac%7B0.85%7D%7B%5Csqrt%7B38%7D%20%7D%20%7D)
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
<u><em>Final answer:-</em></u>
There is no significant difference between their counterparts across the nation.