Answer:
a) sample mean x⁻ = 73
b) The margin of error (M.E) = 3
c) Sample standard deviation(σ) = 8.9404
Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>Step(i)</em></u>:-
Given 90% confidence interval for a population mean is (70, 76)
We know that 90% of confidence intervals are determined by
Given sample size n =26
The degrees of freedom ν=n-1 =26-1=25
…(i)
…(ii)
Adding (i) and (ii) and simplification , we get
<u><em>Sample mean = 73</em></u>
<u><em>Step(ii):-</em></u>
Substitute x⁻ = 73 in equation(i)
<u><em>Margin of error = 3</em></u>
<u><em>Step(iii):-</em></u>
<em>The margin of error is determined by</em>
<em></em><em></em>
<em>we have margin of error = 3</em>
<em>Given sample size 'n' =26</em>
<em></em><em></em>
<em></em><em></em>
<em>Cross multiplication , we get</em>
<em></em><em></em>
<em></em><em></em>
<em>Standard deviation = 8.9404</em>
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