Answer:
<em>The test statistic value  t =  1.64 < 2.0086 at 0.05 level of significance</em>
<em>Null hypothesis is accepted</em>
<em>The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation </em>
<em></em>
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given mean of the population (μ) =  $183,000
Given mean of the sample (x⁻)  = $198,000
Given standard deviation of the sample (S) =  $65,000.
Mean of the sample size 'n' = 51
level of significance  α = 0.05
<u><em>Step(ii):</em></u>-
<u><em>Null hypothesis : H₀</em></u> : There is no significance difference between the means
<em>Alternative Hypothesis :H₁: </em>There is  significance difference between the means
<em>Test statistic</em>
<em>              </em> <em></em>
<em></em>
<em>            </em> <em></em>
<em></em>
<em>           t =  1.64</em>
<u><em>Step(iii)</em></u>
<em>Degrees of freedom  ν = n-1 = 51-1 =50</em>
<em>t₀.₀₅ =  2.0086</em>
<em>The calculated value  t =  1.64 < 2.0086 at 0.05 level of significance</em>
<em>Null hypothesis is accepted </em>
<u><em>Final answer:-</em></u>
<em>There is no significance difference between the means</em>
<em> The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation</em>