Respuesta :
Answer:
The test statistic value 't' = 3.074
Step-by-step explanation:
Step(i):-
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
[tex]t_{\frac{\alpha }{2} } = 1.769[/tex]
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'
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{s}{\sqrt{n} } }[/tex]
[tex]t = \frac{42 -39}{\frac{3.78}{\sqrt{15} } }[/tex]
t = 3.074
The test value of t-statistic t = 3.074
The calculated value t = 3.074 > 1.769 at 0.05 level of significance
null hypothesis is rejected
Alternative hypothesis is accepted
Final answer:-
There is significance difference between the means
