X³+y³+z³=k, for each k from 1 to 100
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Answer:
a) 95% confidence interval estimate of the true weight is (3.026, 3.274)
b) 99% confidence interval estimate of the true weight is (2.944, 3.356)
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
- M is the mean of five successive weightings (3.150)
- ME is the margin of error from the mean
And margin of error (ME) can be calculated using the formula
ME= where
- t is the corresponding statistic in the given confidence level and degrees of freedom(t-score)
- s is the standard deviation of the random error (0.1)
- N is the sample size (5)
Using the numbers 95% confidence interval estimate of the true weight is:
3.150±≈3.150±0.124
And 99% confidence interval estimate of the true weight is:
3.150±≈3.150±0.206