Answer to Question #140007 in Statistics and Probability for Sohyun Ravena

Question

~Include a normal curve/t distribution curve.
~Your final answer must be a concluding statement.

The length of the chicken joy thigh parts, in centimeters, are given below:
7.14, 6.65, 6.76, 6.85, 6.18, 7.47, 7.81, 7.24, 7.20, 6.74
1. Find the sample mean and standard deviation.
2. Find the 95% confidence interval for the mean.
3. Find the 99% confidence interval for the mean.

Answer 1

1) Sum, Σ:70.04

Mean, x̄=Σ/n=70.04/10=7.004

s² = Σ(x_i - x̄)²/N - 1= (7.14 - 7.004)² + ... + (6.74 - 7.004)²10 - 1= 1.936649= 0.215182

s=$\sqrt{0.215182}=0.463877$

2) 95% Confidence Interval (z-value=1.96 - table): x̄±(z₁*s/$\sqrt n$ )= 7.0004 ± 0.288

(6.71 to 7.29)

3)99% Confidence Interval (z-value=2.58 - table):x̄±(z₂*s/$\sqrt n$ )= 7.0004 ± 0.378

(6.62 to 7.38)