The confidence interval for the true mean number of reproductions per hour is (7.5,7.7)
Given mean of 7.6 , standard deviation of 2.2, n=707 and 90% confidence level.
We have to find the confidence interval for the true mean number of reproductions per hour for the bacteria.
α=0.90
μ=7.6
σ=2.2
m=707
α/2=0.45
We have to calculate z value for the p value of 0.45 which is z=1.64.
Margin of error=z*μ/[tex]\sqrt{n}[/tex]
=1.64*2.2/[tex]\sqrt{707}[/tex]
=0.13
Lower level=mean -m
=7.6-0.13
=7.47
after rounding upto 1 decimal
=7.5
Upper level= mean +m
=7.6+0.13
=7.73
after rounding upto 1 decimal
=7.7
Hence the confidence interval is (7.5,7.7) for the true mean number of reproductions per hour.
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