Sampling

Type / Definition / Example
Simple Random Sample
Systematic Sampling
Stratified Random Sample
Cluster Sampling
Voluntary Response Sample
Convenience Sampling

Bias

Rank the types of sampling from highest chance for bias to least chance for bias.

______→______→______→______→______→______

(highest) (lowest)

Do you want bias? yes / no

Therefore, which type of sample is ideal for statistical methods? ______

Central Limit Theorem

2 conditions:

  1. ______
  1. ______

What distribution will sample means have if these 2 conditions are met?______

Can you use CLT to find information relating to a single variable? yes /no

Can you use CLT to find information relating to a sample mean? yes /no

Will all sample means be the same? yes / no

Why? ______

When a population is normal, do you need to use CLT? yes / no

Using a normal distribution to find information

*What is the mean of your sample mean distribution? ______

*What is the standard deviation of your sample mean distribution?______

*To find the probability of obtaining a sample mean, A, find a z-score to correlate with A using

the formula…

______

*Use the z-score table to find the probability related to that z-score.

Confidence Intervals

2 conditions

  1. ______
  1. ______

Equation:

Using a z*value / Using a t* value
______ / ______
Math Symbol / Definition / How to find it
z* / z-value related to α
t* / t-distribution value related to αand degrees of freedom
α / confidence level
__
X / Estimated mean
se(X) or SE(X) / Estimated standard error/Standard Error
df / Degrees of freedom

*assume 95% confidence intervals for the next questions.

Interpretation sentence: (using blanks to fill in based on context)

Also…

____of the confidence intervals made this way would contain the true population mean.

Therefore…

The probability that your confidence interval does NOT contain the true population mean is___

When do you use…

t* values / z* values
What do you need to know to find the value in the t-table? / What do you need to know to find the value in the z-table?

How could you make a confidence interval narrower or wider?

Narrower / Wider

Margin of error =

Hypothesis Testing

The null hypothesis represents ______

The alternative hypothesis represents ______

The 2 options when dealing with null and alternative hypotheses / When do you choose this option? / Sentence to interpret
P-value < α
P-value > α

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

  1. Simple Random Sample
  2. Stratified Random Sample
  3. Systematic Sampling
  4. Cluster Sampling

Put an advertisement in the newspaper asking people to mail in their vote

  1. Simple Random Sample
  2. Voluntary Response Sample
  3. Convenience Sample
  4. Stratified Random Sample

Send a survey to every customer’s home and ask the customer to fill it out and return it

  1. Simple Random Sample
  2. Voluntary Response Sample
  3. Convenience Sample
  4. Stratified Random Sample

Go through the company’s records, selecting every 100th customer. Survey every person chosen.

  1. Simple Random Sample
  2. Stratified Random Sample
  3. Systematic Sampling
  4. 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

  1. Simple Random Sample
  2. Stratified Random Sample
  3. Systematic Sampling
  4. Cluster Sampling

Sponsor a commercial during a TV program and ask people to call in their preferences

  1. Simple Random Sample
  2. Voluntary Response Sample
  3. Convenience Sample
  4. Stratified Random Sample

Go through the company’s records, and select a random 100 customers. Survey every person chosen.

  1. Simple Random Sample
  2. Stratified Random Sample
  3. Systematic Sampling
  4. 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.

OWhat is the probability that a randomly selected American will live to be 80 years old.

OWhat 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.

OCreate a 95% confidence interval for your estimated average.

ODo 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

OWhat is

OWhat is

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-2.83
p-value t 0.006

P-value < t 0.003

P-value > t 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 on your hypothesis based on your sample and these are the test results…

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