1. A confidence interval can be calculated to estimate the population mean when the population is normally distributed or the sample size is greater than 30. Can a confidence interval be calculated for the average number of hours of sleep for the US babies using this requirement? Why?
It needs to be both rather than one or the other.
To determine if a confidence interval can be calculated for the average number of hours of sleep for US babies using the requirement that the population is normally distributed or the sample size is greater than 30, we need to first consider whether the population of US babies' sleep hours is normally distributed or whether the sample size is larger than 30.
If the distribution of sleep hours for US babies is approximately normal, we can proceed with calculating a confidence interval. This would mean that the sleep hours follow a bell-shaped curve, with the majority of babies sleeping around a central value and a decreasing number of babies sleeping more or less.
Alternatively, if the sample size is greater than 30, we can also proceed with calculating a confidence interval. This is due to the Central Limit Theorem (CLT), which states that with a sufficiently large sample size, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population distribution. Therefore, even if the population distribution is not normal, the distribution of sample means will be approximately normal if the sample size is large enough.
To determine if the requirement is met, we would need to assess the properties of the population distribution of sleep hours for US babies or check if the sample size is larger than 30. Once we have this information, we can then determine if a confidence interval can be calculated for the average number of hours of sleep for US babies using this requirement.