150 likes | 162 Views
Learn how to construct confidence intervals for means and understand the differences between means and proportions. Find out how to calculate confidence intervals using the z-distribution and t-distribution. Also, discover how to determine the minimum required sample size.
E N D
Confidence Intervals Means
Remember: In sampling distribution of means….. • Approximately normal if • n is large ( n 30) – CLT • The population is normal
So how will I find a confidence intervals for a mean? How is it different from a proportion?
Suppose you work for a consumer advocate agency & want to find the mean repair cost of a washing machine. You randomly select 40 repair costs and find the mean to be $100. The standard deviation is $17.50. construct a 95% interval for the population mean.
Find the minimum required sample size if you want to be 95% confident that the sample mean is within 2 units of the population mean if the population standard deviation is 4.8.
But what if the sample size is small or the population standard deviation is unknown?
We use the t-distribution if the population standard deviation is unknown. • It’s bell shaped – centered at 0. • Each t-distribution is more spread out than the z-distribution (normal). • As the sample size increases, the spread decreases and actually approaches the normal distribution. • Based on degrees of freedom (df = n-1)
Degrees of freedom: (n-1) • Suppose A + B + C + D = 18 • Thus there are 3 degrees of freedom Free to be anything
The t- distribution compared to the normal distribution • http://www.nku.edu/~longa/stats/taryk/TDist.html • In normal sampling but with t-distribution
The Raman Arches is an Italian restaurant. The manager wants to estimate the average amount a customer spends on lunch. A random sample of 115 customers’ lunch tabs gave a mean of $9.74 with a standard deviation of $2.93. Find and interpret a 90% confidence interval for the average amount spent on lunch by all customers.
A sample of 20 students had a test average of 100 with a standard deviation of 4.2 points. Find and interpret a 90% confidence interval for the average test score for all students on this test.
A random sample of large tents listed in Consumer Reports: Special Outdoor Issue gave the following prices. Find a 90% confidence interval for the mean price of all such tents.