(Solved Homework): •Please determine the 95% confidence interval using the z-interval and the following information…

•Please determine the 95% confidence interval using the z-interval and the following information:

•Mean – 2.75

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•StDev – .025

•Sample size – 35

•Assume the data is normal and please show your work by inserting the equations below or on a separate slide.

Expert Answer

A 95% confidence interval covers 95% of the normal curve — the probability of observing a value outside of this area is less than 0.05. Because the normal curve is symmetric, half of the area is in the left tail of the curve, and the other half of the area is in the right tail of the curve. For a 95% confidence interval, the area in each tail is equal to 0.05/2 = 0.025.

The value z^* representing the point on the standard normal density curve such that the probability of observing a value greater than z^* is equal to p is known as the upper p critical value of the standard normal distribution. For example, if p = 0.025, the value z^* such that P(Z > z^*) = 0.025, or P(Z < z^*) = 0.975, is equal to 1.96

Thus Z value corresponding to 95 % confidence interval = 1.96

Thus Range for 95% confidence interval

= m + /- Z x Sd/ Square root ( n)

m = Mean = 2.75

Sd = Standard deviation = 0.025

N = Sample size = 35

Z = 1.96

Therefore , Range for 95% confidence interval

= 2.75 + / – 1.96 x 0.025/Square root ( 35)

= 2.75 +/- 0.049 /5.916

= 2.75 +/- 0.0083

Thus 95 percent confidence interval = ( 2.7583 , 2.7417 )

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