10 Inference with Means Flashcards
How do you tell if a problem involves means or proportions?
Problems with means almost always say mean or average. Also, they will list a standard deviation somewhere. If you are only given data, it will be a mean problem where you put the data into L1.
What is zap tax?
A useful way to remember that z always goes with proportions and t always goes with x-bar (means).
Technically, when/why do we use t?
When we work with means, using a z-score would require us to know the population st. dev. which we basically never know and so we use t instead.
What is df and how do I find it?
“degrees of freedom”. For one sample problems, it’s just n-1. For 2 samples, you find the df from each sample and take the lower number. Your calculator will actually use a different formula and use a higher df.
How is a t-distribution different from a normal curve?
It will have a lower peak and more area on the tails. The lower the df, the lower the peak.
How do you find the t-value (crit value) for a confidence interval involving means?
Use the t-table and go to the row for your df (n-1)(if there is no row use the closest row with a lower df (never round up). Then go to the correct column using the C% on the bottom of the chart.
How do you find the t-value for a significance test involving means?
Same formula as a z-score but you label it as a t because the p-value will be found using tcdf, not normalcdf. So, stat minus parameter over the st. dev. of the stat.
In the confidence interval formula for means, what is the statistic/point estimate?
1-sample: x-bar i.e. the sample mean
2-sample: x-bar minus x-bar i.e. the difference of the two sample means.
Usually these numbers are given to you but sometimes you’ll need to put data in L1 and then the calculator will give you these numbers when you run the interval.
How do you check the “normal”/large count condition for means?
n >= 30 (the central limit theorem) OR the problem states that the population is approx normal OR if n < 30 the sample would need to have no strong skew or outliers. Note: you may need to make a quick dotplot of the data on your paper to justify that claim.
In what scenarios would we not need to test the 10% condition (n<10% of all…)?
the 10% condition is to show that sampling was independent. So if you aren’t sampling (like doing an experiment) you would just say that the trials were independent.
When doing a significance test for means, how do you know which range of values the p-value is in?
If you use the calculator to do the test, just get the p-value and see which range it is actually in. If you use the t-table to find the p-value, the best you can do is use the range of values at the top of the table.
