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Svetllana [295]
3 years ago
9

According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. As

sume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether 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, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Mathematics
1 answer:
Lady_Fox [76]3 years ago
4 0

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>t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }<em></em>

<em>            </em>t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }<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>

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