Answer:
The test statistic value 't' = 3.074
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given sample size 'n' = 15
mean of the Population 'μ' = $39
mean of the sample x⁻ = $42
standard deviation of the sample 's' = $3.78
Degrees of freedom ν = n-1 = 15-1 =14
![t_{\frac{\alpha }{2} } = 1.769](https://tex.z-dn.net/?f=t_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3D%201.769)
Null hypothesis : There is no significance difference between the means
H₀ : x⁻ = 'μ'
Alternative hypothesis : There is significance difference between the means
H₀ : x⁻ ≠ 'μ'
<u><em>Test statistic </em></u>
![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{42 -39}{\frac{3.78}{\sqrt{15} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B42%20-39%7D%7B%5Cfrac%7B3.78%7D%7B%5Csqrt%7B15%7D%20%7D%20%7D)
<em>t = 3.074</em>
The test value of t-statistic <em>t = 3.074</em>
<em>The calculated value </em> <em>t = 3.074 > 1.769 at 0.05 level of significance</em>
<em>null hypothesis is rejected</em>
<em>Alternative hypothesis is accepted</em>
<u><em>Final answer</em></u><em>:-</em>
There is significance difference between the means
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