Consider a population that is approximately normally distributed with unknown population mean and unknown population standard deviation. A sample of \(450\) observations has a sample mean of \(\bar{x}=62\) and standard deviation of \(52\). Find a \(95 \%\) confidence interval for the population mean. (Interpret your answer within the context of the problem, use complete sentences)
Suppose average pizza delivery times are normally distributed with an unknown population mean. A random sample of \(28\) pizza delivery restaurants is taken and has a sample mean delivery time of \(36\) minutes with standard deviation of \(6\) minutes. Find a \(90 \%\) confidence interval for the population mean delivery time. (Interpret your answer within the context of the problem, use complete sentences)
To find the \(t\)-scores corresponding to a \(70 \%\) confidence level, what additional information do you need to know?
Provide a range of \(t\)-scores that captures \(80 \%\) of all \(t\)-scores
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation. A random sample of \(36\) scores is taken with an mean score of \(72\) and standard deviation of \(10\). Find a \(98 \%\) confidence interval for the mean exam score of the population. (Interpret your answer within the context of the problem, use complete sentences)