Question

Use the accompanying descriptive statistics output to calculate a 99% lower confidence bound for true average ultimate tensile strength, and interpret the result.

N Mean Median TrMean StDev SE Mean
153 135.39 135.40 135.41 4.59 0.37
Minimum Maximum Q1 Q3
122.20 147.70 132.95 138.25

Answer 1

To calculate the 99% lower confidence bound for the true average ultimate tensile strength, subtract the product of Z-score and standard deviation from the mean.

Step-by-step explanation:

To calculate a 99% lower confidence bound for the true average ultimate tensile strength, you can use the formula:

Lower Confidence Bound = Mean - (Z * (Standard Deviation / Square Root of Sample Size))

Using the given descriptive statistics, the formula would be:

Lower Confidence Bound = 135.39 - (2.33 * (4.59 / Square Root of 153))

Calculating the value, the lower confidence bound for the true average ultimate tensile strength is approximately 134.27. This means you can be 99% confident that the true average ultimate tensile strength is at least 134.27.

Answer 2

Lower confidence boundary = 134.525

μ ≥ 134.525

Step-by-step explanation:

From the data:

Sample size, n = 153

Sample mean, xbar = 135.39

Standard deviation, s = 4.59

Zcritical at 99% = 2.33 (one sided)

Confidence interval :

Xbar ± standard Error

Standard Error = Zcritical * s/√n

Standard Error = 2.33 * 4.59/√153 = 0.865

Lower boundary:

Xbar - standard error

135.39 - 0.865 = 134.525

μ ≥ 134.525

We Can be 99% confidence that the true average ultimate tensile strength is atleast 134.525