Dependent vs. Independent Means

μd = 0 is for...

• Dependent Means Ho

• Dependent Means Ha

• Independent Means Ho

• Independent Means Ha

We are looking at studying heart-rate of males before and after drinking caffeine.

• Dependent

• Independent

• Simple Linear Regression

• T-Pain

We are observing the effect winter has on the average weight of a group of bears in a national park. Compared to before, we expect them to weigh less after winter. What is Ha?

We observe the weight of bears before and after winter:

xbar difference = 45 lbs

s difference= 4.7

n = 30

Find and interpret the confidence interval (95%)

Answer explanation

(+, +) --> Mu1 is higher

We are 95% confident that the weight of all bears in the national park are 43.25 to 46.76 pounds higher before winter compared to after winter.

We are 95% confident that the weight of all bears in the national park decreases after winter.

We observe the weight of bears before and after winter:

xbar difference = 45 lbs

s difference= 4.7

n = 30

Calculate the standard error

• 0.67

• 0.73

• 0.86

• 0.9

To create one list from two lists of data, we do L1 - L2 = L3 in our calculator. What statistical tests are these required for?

• Dependent means

• Independent means

• Both

• Neither

We observe the weight of bears before and after winter:

xbar difference = 45 lbs

s = 4.7

n = 30

We predict bears will weigh less after winter. Write a conclusion with your results

Answer explanation

p = <0.001

t = 52.44

We have significant evidence that bears weigh less after winter.

We are comparing the lifespan of tortoises (pop 1) and turtles (pop 2). We expect their lifespans to be different.

• Mu1 > Mu2

We are comparing height of pine trees in the midwest (Pop 1) vs. the height of pine trees in the west of the United States.

Midwest: xbar = 63.5, s = 6, n=500

West: xbar = 70.4 s = 4, n=500

Create a 95% confidence interval

• (-9.66, -8.41)

• (-7.53, -6.27)

• (6.27, 7.53)

• (8.41, 9.66)

Answer explanation

We are 95% confident that all Midwest pine trees are, on average, shorter than trees in the west.

We are 95% confident that all Midwest pine trees are 6.27 to 7.53 feet shorter than trees in the west.

We are comparing height of pine trees in the midwest (Pop 1) vs. the height (in feet) of pine trees in the west of the United States.

Midwest: xbar = 63.5, s = 6, n=500

West: xbar = 70.4 s = 4, n=500

Determine if the two are different. What is Ha? Are they statistically different?

• mu1 > mu2

  Reject Ho

• mu1 < mu2

  Fail to reject Ho

Answer explanation

We are 95% confident that all Midwest pine trees are, on average, shorter than trees in the west.

We are 95% confident that all Midwest pine trees are 6.27 to 7.53 feet shorter than trees in the west.