Answer:
The answer is below
Step-by-step explanation:
The z score is used to determine by how many standard deviations the raw score is above or below the mean.
Given that: sample size (n) = 6, standard deviation (σ) = 0.09 mm, mean (μ) = 2.34 mm
The confidence interval = 90% = 0.9
α = 1 - 0.9 = 0.1
α / 2 = 0.05
The z score of 0.05 is the same as the z score of 0.45 (0.5 - 0.05) which is 1.645.
The margin of error is given as:
[tex]E=Z_{\frac{\alpha}{s} }*\frac{\sigma}{\sqrt{n} }[/tex]
[tex]E=1.645*\frac{0.09}{\sqrt{6} }=0.06\ mm[/tex]
The confidence interval = μ ± E = 2.34 ± 0.06 = (2.28, 2.40)
The confidence interval is between 2.28 mm and 2.4 mm
