You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 35 home theater systems has a mean price of $145.00. Assume the population standard deviation is $18.10. Construct a 90% confidence interval for the population mean. The 90% confidence interval is ( ). (Round to two decimal places as needed.)
Confidence Interval: In statistics, we can say a range of values of the specified population parameter that is lies within it with some confidence is known as Confidence Interval. They can take any number of probability limits, with the most common being a 90%, 95% or 99% confidence level. Confidence level is denoted by 1 - . The probability that the confidence interval actually contains the population parameter.
The most commonly used confidence levels are 90%, 95% and 99%.
If you have set of data is under 30 (n < 30), you want to use t-distribution instead of the normal distribution(z-score) to construct your confidence interval and Vice-versa.
Then the formula for constructing the confidence interval at 90% confidence level is given by
where x-bar is sample mean
s is sample standard deviation
n is sample size and
z/2 is the Critical value.
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