Final Review Examples

Unit 1

Population, Parameter, Sample, Statistic.

You are looking at the average age of all NFL players, you select 20 random athletes to see how old they are. The average age of the 20 athletes is26. The true average age of the NFL is 28.

Population: ______

Parameter: ______

Sample: ______

Statistic: ______

Your dog can jump 2.5 feet. This leads you to believe your dog can jump farther than any other dog. However, the American record book has a dog that can jump 6.48 feet.

Population: ______

Parameter: ______

Sample: ______

Statistic: ______

The Iowa state football team has an average number of points per game of 17. The Big 12 average points per game is 32. You then conclude the ISU offense is pretty low scoring.

Population: ______

Parameter: ______

Sample: ______

Statistic: ______

Visuals

Based on this data of different scores in Stat 226, draw a box plot.

46 32 58 68 72 75 76 77 78 78 82 85 85 85 89 89 90 91 94 97

Draw a histogram for the data. Describe the distribution

In class, you ask people what their favorite animal is and come up with this data. Make a visual that is fitting for this kind of data.

Animal / #of People
Zebra / 5
Hippo / 3
Elephant / 8
Ram / 4
Sea Lion / 12
Flamingo / 5
Leopard / 1
Koala / 9

Normal Distribution

The times for the 200m sprint for the mens track team is normally distributed with a mean of 24.2 sec. and a standard deviation of 1.2 seconds.

a)What time can 50% of the teammates complete a 200m in?

b)What percent of runners can complete a 200mbetween 23.0 seconds and 25.4 seconds?

c)Jim brags that he can run faster than 95% of his teammates? What would his time be if he’s right?

d)If Joeis wanting to make the team and he can run the 200m in 28.2 seconds, do you think he would make the team?

e)What is the probability that one of the boys will beat the opponents’ fastest sprinter who can do the 200m in 22 sec?

Life span of a Calliope hummingbird is normally distributed with an average span of 6 years and a standard deviation of 0.15 years.

a)What is the age that at least 43% of hummingbirds live to?

b)How old is the youngest of the oldest 25% of hummingbirds?

c)If you have a hummingbird who is 6.21 years old, what percent of hummingbirds are older than him?

d)If you want to have a hummingbird as a pet, what is the probability it will die in your college career(assuming 4 year college and getting a baby hummingbird)?

e)If you only want a pet that lives for a few years, do you think you would get a hummingbird?

Unit 2

Sampling

You are trying to see which school Iowans like more – the panthers, the hawkeyes, or the cyclones.

Give an example as to how you would obtain each kind of sample

Voluntary Response

Convenience Sample

Stratified Random Sample

Simple Random Sample

Systematic Sample

Cluster Sample

Non-normal distributions

The life expectancy in America is non - normal with an average of 72years and a standard deviation of 15 years

What is the probability that a randomly selected American will live to be at least 80 years old?

What is the probability that you will obtain a random sample of 45 people who live to be an average of 80 years old?

If you obtained a sample mean that has a 15% chance of happening, what value(s) might your sample have had as the average age of the group.

Confidence intervals

You are trying to evaluate how accurate the gas pumps in Ames are. So, you pour gas in to a measurement cup and see how close it is to the 15 gallons it said you had poured out. You obtain 32 samples and find that the average amount of gas you got in your measuring cup was 14.5 gallons with a sample standard deviation of 1.3 gallons.

Create a 95% confidence interval for the true amount of gas you get when the machine says 15 gallons?

Do you think the company is ripping you off?

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. Your sample of 100 students pays an average of $18,856 and has a sample standard deviation of $8,750.

What is your null hypothesis?

What is your alternative hypothesis?

Calculate a test-statistic.

You run the test and obtain the following…

p-value t 0.006

P-value < t 0.003

P-value > t 0.997

What can you conclude at an alpha level of 0.05?

Unit 3

Linear Relationships

You are working for a ski resort. You want to know if the amount of snow you get is related to the amount of sales you get that day.

You look at 20 different days and obtain the following scatterplot. (snow in in., sales in $

The line of best fit is = 103.23x + 25.32, with an R-squared value of 0.8831.

Describe the slope

the intercept,

and the r-squared.

Find a 95% confidence interval for the slope of the line and interpret what it means.

(t* = 2.14)

You run a hypothesis test on the data and obtain the following results.

Fill in the t-ratio

Term / Estimate / Std error / t-ratio / p-value
Snow / 103.23 / 43.89 / 0.0004

What are your conclusions based on the hypothesis test?

If you were expecting a day with 12 inches of snow, how much money would you expect to make?

If you were wanting to make $750 tomorrow, how much snow should you hope and pray for?

If you were expecting a blizzard with 63 inches, how much money should you expect to make? Do you think you would actually make that much? What kind of problem is this an example of?