Sampling
A company is trying to see if it it’s customers would prefer to expand their clothing section or their home
store section.
Why would we take a sample? ____________________________________________________
Randomly select one store and ask 30 of the customers at this store their opinion
A. Simple Random Sample
B. Stratified Random Sample
C. Systematic Sampling
D. Cluster Sampling
Put an advertisement in the newspaper asking people to mail in their vote
A. Simple Random Sample
B. Voluntary Response Sample
C. Convenience Sample
D. Stratified Random Sample
Send a survey to every customer’s home and ask the customer to fill it out and return it
A. Simple Random Sample
B. Voluntary Response Sample
C. Convenience Sample
D. Stratified Random Sample
Go through the company’s records, selecting every 100th customer. Survey every person chosen.
A. Simple Random Sample
B. Stratified Random Sample
C. Systematic Sampling
D. Cluster Sampling
Randomly select 20 customers from each store. Send each a survey and follow up with a phone call if
they do not return the survey within a week
A. Simple Random Sample
B. Stratified Random Sample
C. Systematic Sampling
D. Cluster Sampling
Sponsor a commercial during a TV program and ask people to call in their preferences
A. Simple Random Sample
B. Voluntary Response Sample
C. Convenience Sample
D. Stratified Random Sample
Go through the company’s records, and select a random 100 customers. Survey every person chosen.
A. Simple Random Sample
B. Stratified Random Sample
C. Systematic Sampling
D. Cluster Sampling
Central Limit Theorem
The life expectancy in America is non - normal with an average of 72years and a standard deviation of 15
years.
O
What is the probability that a randomly selected American will live to be 80 years old.
O
What is the probability that you will have obtain a random sample of 45 people with a sample
mean of 98 years.
Confidence Intervals
A box of Lucky Charms promises an average 15 oz of cereal per box. You want to test this claim, so you
tested a sample of 40 boxes. The average amount of cereal in these 40 boxes was 13 oz with an
estimated s = 8.8oz.
O
Create a 95% confidence interval for your estimated average.
O
Do you think the company is holding up to their promise?
Interpret this Interval:
In trying to predict average body temperature of Americans, I got a 95% confidence interval of…
( 96.9 99.3)
_________________________________________________________________________
Hypothesis Testing
The average college student pays $20,335 per year in tuition. In order to see if Iowa State costs are less
than the national average, a random sample of 100 ISU students is taken
O
What is 𝐻𝑜
O
What is 𝐻𝐴
Your sample of 100 students pays an average of $18,856 and has a sample standard deviation of $8,750.
When you run a hypothesis test you obtain the following output…
t-stat
p-value ≠ t
P-value < t
P-value > t
-2.83
0.006
0.003
0.997
What can you conclude about ISU tuition costs?
Putting it all together
The Situation
You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing
to offer it if it seems to have a customer ranking of at least 7.5 (out of 10).
The Basics
What is the population?
What is your parameter?
What to Do
You decide to take a sample of 125 of your customers.
What type of sample should you take?
Can you still make assumptions even if the population distribution is non-normal?
What are you trying to prove?
What is your Null hypothesis and alternative hypothesis?
Let’s prove it!
Your sample yields an average of a 6.8 rating. Your sample standard deviation is 2.15.
Create a 95% confidence interval for the population parameter.
You perform a hypothesis test with 𝛼 = 0.05 on your hypothesis based on your sample and these are
the test results…
𝑋̅ = 6.8
t-stat = -3.64
p-value < t = 0.043 p-value > t = 0.957 p-value ≠ t = 0.086
Conclusion
Are you going to offer this new sports channel?
- Using confidence interval
-
Using your hypothesis test