• My car averages 28 miles to the gallon on the highway. I switch to a new motor oil that is advertised to increase gas mileage. After driving for a couple of months I’m going to determine whether or not my average miles to the gallon has increased.

• The diameter of a spindle in a small motor is supposed to be 5 mm, otherwise it will not work properly. The manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target.

• Your friend claims to be a 90 % free throw shooter, but you doubt his athletic prowess. Your friend agrees to go down to the gym and shoot some free throws to convince you he’s the real deal.

• A physical education instructor teaches basketball skills to two groups. For Group A, she is complimentary and encouraging. For Group B, she acts cool and neutral. The instructor hopes to show that a positive attitude results in a higher mean score on a test of basketball skills.

• A sociologist asks a large sample of high school students which academic subjects they like best. She suspects that a higher percent of males than of females will name mathematics as their favorite subject.

H0: = #

Ha: > #

H0: = #

Ha: < #

H0: = #

Ha: #

“EXTREME”

As large as z, or larger.

P(Z z) = 1 P(Z z)

As small as z, or smaller.

P(Z z)

As far from the center of the distribution as z, or further.

P(|Z||z|) = 2(1P(Z |z|))

CIs and Two-Sided Tests

• A level two-sided significance test rejects a hypothesis H0: = 0 if and only if the value 0 falls outside a level (1) confidence interval for .