Question

ters, Statistical Intervals for a Single Sample Prok cm : An engineer is analying the compressive strength of concrete. Compressive strength is normally distributed with σ2 1000(psi)2. A random sample of 12 specimens has Workshop: Point Estimation of Paramet or',, a mean compressive strength of x 3250 psi. (a) Construct a 95% two-sided confidence interval on mean compressive strength (b) Construct a 99% two-sided confidence interval on mean conpressive strength. Compare the width of this confidence interval with the width on the one found in part (c) Suppose that it is desired to estimate the compressive strength with an error that is less than 15 psi at 99% confidence. What sample size should be used? Problem II: Statistical Intervals for a Single Sample I. Confidence Interval on Mean, Variance Unknown When working with a data sample of a particular measurement taken from a population, you can estimate the mean and variance of that parameter in the population. These estimates are cealled the sample mean and sample variance (or its square root, the sample standard viation). With the estimate, as with individual measurements, there is associated with a value. A two-sided confidence interval on the mean gives us a measure of the certainty that the uncertainty true mean will be within an interval of the calculated sample mean. Today, we will be working with data that involves chocolate chip cookies

Answer 1

(Q1)

(a)

n = 12     

x-bar = 3250     

s = 31.6227766     

% = 95     

Standard Error, SE = σ/√n =    31.6227766016838 /√12 = 9.128709292

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 9.12870929175277 = 17.89194144

Lower Limit of the confidence interval = x-bar - width =      3250 - 17.8919414371716 = 3232.108059

Upper Limit of the confidence interval = x-bar + width =      3250 + 17.8919414371716 = 3267.891941

The 95% confidence interval is [3232.11 psi, 3267.89 psi]

(b)

n = 12     

x-bar = 3250     

s = 31.6227766     

% = 99     

Standard Error, SE = σ/√n =    31.6227766016838 /√12 = 9.128709292

z- score = 2.575829304     

Width of the confidence interval = z * SE =     2.57582930354892 * 9.12870929175277 = 23.5139969

Lower Limit of the confidence interval = x-bar - width =      3250 - 23.513996897276 = 3226.486003

Upper Limit of the confidence interval = x-bar + width =      3250 + 23.513996897276 = 3273.513997

The 99% confidence interval is [3226.47 psi, 3273.51 psi]

The 99% confidence interval is wider than the 95% confidence interval

(c)

For 99% confidence, z = 2.5758

E = 15

Sample size N = (z * σ/E)^2 = (2.5758 * √1000 /15)^2 = 30

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