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Stats 8.3 (2017).notebook March 04, 2018
If given σ If not given σ then use Sx
Error < μ < + Error
Review
confidence interval
Summarize with a sentence that pertains to the population mean
look in Student's t Distribution chart in the cover of the book for this number. Remember when you use the t chart you must use degree of freedom (d.f.)
Stats 8.3 (2017).notebook March 04, 2018
LARCENY AND YOU! Thirty small communities in Connnecticut (population per 10,000 each) gave an average of 138.5 reported cases of larceny per year. Assume that σ is known to be 42.6 cases per year.Find a 95% Confidence interval for the dataGive an interpretation of your results in context to this problem
8.18.2 Review
We are 95% confident if we found how many cases of larceny happened in ALL small communities in Connecticut, and averaged those numbers, that population average would be between ____________ and ____
PULL
123.26 153.74
E = 15.24
Error < μ < + Error 138.5 15.24 < μ < 138.5 + 15.24
123.26 < μ < 153.73
Stats 8.3 (2017).notebook March 04, 2018
2) A random sample of 10 small popcorns form the movie theater. weighed (in ounces):
6.2 4.7 5.9 6.1 5.85.3 5.7 5.2 5.1 5.6
Find a 90% confidence interval for the mean weight of all small popcorns served at the theater. Give an interpretation.
We are 90% sure if we were able to weigh all small popcorns at this movie theater and average those weights, the population average weight would be between 5.28 and 5.84 ounces
pull:
Stats 8.3 (2017).notebook March 04, 2018
The students will be able to estimate p (population proportion) in the binomial distribution.
What we already know:The binomial distribution relies on the number of trials and the probability of success.
The normal distribution is a good approximation for the binomial distribution.
We will be estimating p assuming n has already been selected.
What we are doing next:
Population Samplemean μproportion p
we were estimating using
today we estimate using
Stats 8.3 (2017).notebook March 04, 2018
Large Sampless ≈ σ np > 5 nq > 5n = number of trialsp = the proportion of the population with a certain
attribute (probability of success) = the proportion of the sample with a certain
attribute (probability of success)r = the number of sample items having the
attribute (# successes in n trials)
Estimating the mean with DISCRETE data.
2. Write interval:
Stats 8.3 (2017).notebook March 04, 2018
Estimating p with
1. Find error using:
2. Write interval:
3. Write an explanation:
We are _____ % sure ...
Round all proportions to 4 decimal places!
Stats 8.3 (2017).notebook March 04, 2018
EX: Find the margin of error given each of the following variables.
Estimating the mean with DISCRETE data.
Stats 8.3 (2017).notebook March 04, 2018
11
Suppose we sample 188 books sold at a bookstore and found 66 of 188 were murder mysteries. Find a 90% confidence interval for p, the proportion of all books sold by this bookstore that are murder mysteries.
n = r =
np ≈ 188(0.35) = 65.8nq ≈ 188(0.65) = 122.2
= 0.0573
Confidence Interval
0.3511 0.0573 < p < 0.3511 + 0.0573 0.2938 < p < 0.4084
We are 90% sure that population proportion of books that are murder mysteries at this bookstore is between 29.38% and 40.84%
pull
Stats 8.3 (2017).notebook March 04, 2018
The manager of the dairy section of a large supermarket took a random sample of 250 egg cartons and found that 40 cartons had at least one broken egg.
a) Let p be the proportion of egg cartons with at least one broken egg out of the population of all egg cartons stocked by this store. Find a point estimate for p (find ) .
n = r =
b) Find a 95% confidence interval for p. Give a brief interpretation of the meaning of your confidence interval.
Calulator1. STAT2. TEST3. 1PropZInt...4. Enter stats
skip for now:
We are 95% sure the population proportion of egg cartons in this store with at least one broken egg is between 11.46% and 20.54%
pull:
250 40 = .160025040
1 .16 = .8400
Stats 8.3 (2017).notebook March 04, 2018
The U.S. Department of the Interior is checking cattle on the Windgate open range in Montana. A random sample of 900 cattle shows that 54 are undernourished.
a) Let p represent the proportion of undernourished cattle on the Windgate range. Find a point estimate for p. (find p)
b) Find a 0.99 confidence interval for p.
Stats 8.3 (2017).notebook March 04, 2018
pg 433 #1,2,8
HOW MUCH DO MELPS WEIGH?? Adult wild melps captured and released for the first time in the Tarablahmi gave the following weights (lbs):
68 104 128 122 60 64
a) Find the mean and standard deviation of the data.b) Find a 75% Confidence interval for the datac) Give a brief interpretation of your results in context to this problem
Review question
1) A random sample of high school students who drive to school had average drive length of 2.18 miles with a known population standard deviation of .21 miles.Find a 95% confidence interval for the population mean length that a high school student travels to school.
74.68 107.32