PSY202H5 Lecture Notes - Lecture 2: Confidence Interval, Sampling Distribution, Design Of Experiments
1
Lecture 2
Example
• Hence t transform of mean is
• If we don’t know the population distribution we cant use z we have to use t distribution
• The t distribution is going to depend on the sample size n
• A. Sampling distribution for the y bar for samples of size n=100 from a distribution of
normally-distributed measures, y, whose population mean was =50, and whose
population std. was . The green lines specify the values of the mean that enclose
95% of the central area of the distribution
• B. The z transform of the sampling distribution of the mean shown in A. The green lines
enclose 95% of the central area of the z distribution.
Working with inequalities
• 10> x>4 is the same thing as 4<x<10
• if 4
• if 4<x<10 then 4+3<
o if we add to each side of the inequality it doesn’t change it
Formula to compute confidence intervals:
When to use confidence intervals
• When you don’t know the population mean but are trying to estimate the population
mean using the sample mean
• To compute a z or t- based confidence interval we must have reason to believe that the
sample mean is normally distributed
find more resources at oneclass.com
find more resources at oneclass.com
2
• Use a z- based confidence when we know the population std. or when n is very very large
(n > 1000)
Example 2
• A politician is going to have to vote whether or not to legalize gay marriages. He is afraid
that if he makes the wrong decision he will lose the next election. So he conducts a
random sample of the voters in his district to find out whether they are in favour of gay
marriage. Of the 3490 people polled, 2166 said they were in favor of gay marriage.
o Estimate of proportion of people in favour 2166/3490
• What kind of experimental design is this?
o Single group design, one measure per subject
• What kind of data is being collected?
o Binary
• Use z instead of t because they would both yield the same results, since the sample size is
so large
• Does the politician have a hypothesis about the proportion of voters favouring gay
marriages?
o No, he does not have a null hypothesis in mind. He simply wants to test the waters
before voting.
• What is our estimate of the proportion of voters favouring gay marriages?
o Our estimate of the proportion of voter favouring gay marriages is
o
• How is this estimate of the proportion favouring gay marriages distributed and why?
o The obtained proportion will be normally distributed because the sample size n is
very large
• Do we know the standard deviation of this proportion?
o No we don’t know the true value of p. However, because our estimate of p is
based on such a large sample we know that
o
o is distributed according to z.. Hence we can construct a confidence interval basec
on the z distribution
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Lecture 2: hence t transform of mean is, the t distribution is going to depend on the sample size n. If we don"t know the population distribution we cant use z we have to use t distribution: a. Sampling distribution for the y bar for samples of size n=100 from a distribution of normally-distributed measures, y, whose population mean was =50, and whose population std. was =20. The green lines specify the values of the mean that enclose: b. The z transform of the sampling distribution of the mean shown in a. 95% of the central area of the distribution enclose 95% of the central area of the z distribution. Working with inequalities: 10> x>4 is the same thing as 4
