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Lecture 1

STATS 13 Lecture Notes - Lecture 1: Ann Perkins, Sampling Distribution, Null Hypothesis


Department
Statistics
Course Code
STATS 13
Professor
Tsiang, Mike
Lecture
1

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Discussion Notes!
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Midterm Review!
suppose hypothesis is μ = .25 and μ < .25, which standardized statistic = strongest evidence against the null hypothesis and
for the alternative!
t= -1.80 bc highest absolute value and bc its less than so it needs negative!
mean cost of wedding is $698. in a sample of 40 weddings, it was found the average cost of flowers was $734 with a
standard deviation of $102. with a 95% confidence interval for the mean cost of a wedding is $701 to $767!
what is the mean cost or a wedding based on the confidence interval with an α level of .05!
1 - α means 95% confidence interval!
answer: the mean cost of flowers for a wedding in the US is more than $698!
confidence intervals!
what is the best interpretation of the 95% confidence interval!
if we were to do this survey a great many times, about 95% of the resulting confidence intervals would include the
mean cost of flowers for all weddings in the US!
choose the statement the best describes what is meant when we say the sample mean is unbiased when estimating the
population mean!
on av the mean of the expected is = to the population!
on average, the sample mean is the same as the population!
ann perkins on time ambulance response within 3 minutes, overall proportion of on time responses in the city as a whole is .
45 π = .45 π < .45!
suppose her sample is 50 but only 20 are on time!
to carry out a simulation based test, ann collects red and blue poker chips and echoes that the red chips represent on
time response and blue represents not on time responses. she plans to put a large number of poker chips and takes out
50 random chips. what percentage of the chips in the box should be blue?!
on time 45 so red = 45 blue should be 55%!
according to the centers for disease control, about 18% of adolescents age 12-18 are obese. supposed we take a random
sample of 30 adlescents and find the proportion in our sample who are obese. !
suppose we make a dot plot of the sample proportions. would the do plot be a visualization of the population
distribution, distribution of the sample, or sampling distribution!
sampling distribution!
if instead of 30 we took a sample of 300, how would the distribution as visualized by the dot plot change !
as we increase sample size, we get closer to the normal disitrbuion !
the spread will decrease!
a. the center would be about the same but the spread would be smaller and the shape would be close to the
normal distribution !
JJ lips come over of JJ diner in pawnee indiana wants to make a new wae that is made with batter that has been infused
with whipped cream. he makes 800 waes and some unknown proportion of them were made with the new whipped cream
infused wae batter. each wae was made individually so no two wae was stuck together. supposed leslie orders 30
waes from JJ diner. jj randomly selects 30 waes from the 800 and she notes that 90% of them were infused with
whipped cream!
she wants to use the empirical rule but one of the validity conditions is not satisfied!
sample is not random X states that it is random!
sample is not large enough ** this is the answer!
bc she needs to meet the condition of 10 successes and 10 failures but her # of successes is .9 (30( = 27 but
number of failures is 3!
population not large enough X n > 20 // 20*30 = 600 < 800!
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tip code but label for category
not absolute scale
sample mean depends on how you take sample
mean may vary alot
SD of sample dist fpop standard deviation
NNLM
on average sample mean pop mean
95 Cont Int
Want Smaller MoEW
lo tr in coutid
changing It changes confid
larger nwill go down so cout stays
same bit MOE smaller
just 9larger random sample
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