2. The following observations of the spring constant of a steel spring were made

Question

2. The following observations of the spring constant of a steel spring were made (in N/m): 695 719 726 731 735 755 757 758 761 762 762 770 779 781 796 797799 801 822 837 937 (a) Calculate the sample mean , the maximum likelihood variance , and sample variance s2. (As a challenge, use Matlab, R or alternative software to do this) (b) Assuming a normal distribution, give 95% confidence intervals for the mean and standard deviation. (c) Give 99% confidence intervals for the mean and standard deviation.

Explanation / Answer

Solutiona:

springcons <- c(695,719,726,731,735,755,757,758,761,762,762,770,779,781,796,797,799,801,822,837,937)
print(springcons)
samplemean <- mean(springcons)
samplemean
samplevariance <- var(springcons)
samplevariance
MLE <- var(springcons)/length(springcons)
MLE
#95% CI for mean
t.test(springcons,conf.level = 0.95)
#99% CI for mean

t.test(springcons,conf.level = 0.99)

Soolutions:

sample mean=775.2381

sample variance=2578.49

MLE variance= 122.7853

Solutionb:

95% confidence interval for mean is

752.1238 and 798.3523

Solutionc:

99% confidence interval for mean is

743.7093 and 806.7669

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