Asked by kayla wallace on Jul 06, 2024
Verified
A sample of 144 cans of coffee showed an average weight of 32 ounces.The standard deviation of the population is known to be 1.4 ounces.
a.
Construct a 68.26% confidence interval for the mean of the population.
b.
Construct a 97% confidence interval for the mean of the population.
c.
Discuss why the answers in Parts a and b are different.
Confidence Interval
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter.
Standard Deviation
A statistical measure of the dispersion or spread of data points in a data set, indicating how much the individual data points differ from the mean.
Population Mean
The average of a set of characteristics or numbers in the entire population.
- Understand the basic structure and elements of interval estimates for population means and proportions.
- Acquire knowledge about the impact of sample size and confidence levels on the margin of error and the determination of confidence intervals for population means and proportions.
- Comprehend the principle of the level of significance (α) and its association with confidence intervals.
Verified Answer
a.
31.88 to 32.12 ounces
b.
31.75 to 32.25 ounces
c.
As the level of confidence increases, the confidence interval becomes wider.
Learning Objectives
- Understand the basic structure and elements of interval estimates for population means and proportions.
- Acquire knowledge about the impact of sample size and confidence levels on the margin of error and the determination of confidence intervals for population means and proportions.
- Comprehend the principle of the level of significance (α) and its association with confidence intervals.
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