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Answer:
a. 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can is 0.998±0.0055
b. <u>No,</u> because a 1-gallon paint can containing exactly 1-gallon of paint lies <u>within</u> the 95% confidence interval.
c. Yes. The population amount of paint per can is assumed normally distributed, because confidence interval calculations assume normal distribution of the parameter.
d. 90% confidence interval is 0.998±0.0046. The answer in b. didn't change; 1-gallon paint can containing exactly 1-gallon of paint lies <u>within</u> the 90% confidence interval. The manager <u>doesn't have</u> a right to complain to the manufacturer.
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
M is the sample mean amount of paint per 1-gallon can (0.998 gallon)
ME is the margin of error from the mean
And margin of error (ME) can be calculated using the equation
ME= where
- z is the corresponding statistic in the 95% confidence level (1.96)
- s is the sample standard deviation (0.02 gallon)
- N is the sample size (50)
Then ME=≈0.0055
95% confidence interval is 0.998±0.0055
90% confidence interval can be calculated similary, only z statistic is 1.64.
ME= ≈0.0046
90% confidence interval is 0.998±0.0046