Answer:
95 percent confidence interval for μ is determined by
(60.688 , 69.312)
a) be the same
Step-by-step explanation:
Step (i):-
Given data a random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph.
The sample size is n= 121
The mean of the sample x⁻ = 65mph.
The standard deviation of the population is 22 mph
σ = 22mph
Step (ii) :-
Given The 95 percent confidence interval for μ is determined as
(61.08, 68.92)
we are to reduce the sample size to 100 (other factors remain unchanged) so
given The sample size is n= 100
The mean of the sample x⁻ = 65mph.
The standard deviation of the population is 22 mph
σ = 22mph
Step (iii):-
95 percent confidence interval for μ is determined by
[tex](x^{-} - 1.96\frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} } )[/tex]
[tex](65 - 1.96\frac{22}{\sqrt{100} } , 65 + 1.96 \frac{22}{\sqrt{100} } )[/tex]
(65 - 4.312 ,65 +4.312)
(60.688 , 69.312) ≅(61 ,69)
This is similar to (61.08, 68.92) ≅(61 ,69)
Conclusion:-
it become same as (61.08, 68.92)
