## Lesson 19: One-Tail vs Two-Tail Hypothesis Testing

November 7, 2016

Mon, Nov 7

Review:

- Significance Testing
- Election assignment

Presentation:

- Hypothesis testing: 1-tail vs 2-tail
- Example 6.16 (p. 385)
- Ho: μ = 450, Ha: μ > 450, x-bar = 461, n=500, σ = 100, α = 0.05

- Example problems
- Ho: μ = 25, Ha: μ > 25, x-bar = 28.2, n=64, σ = 8.4, α = 0.05
- Ho: μ = 7.4, Ha: μ < 7.4, x-bar = 6.9, n=24, σ = 1.2, α = 0.05

Activity:

Determine whether it’s a 1-sided or 2-sided hypothesis test and solve. Report p-values and determine if you can reject or must fail to reject the null hypothesis.

- The college bookstore tells students the average textbook price is $52 with a standard deviation of $4.50. A group of students thinks the average price is higher. In order to test the bookstore’s claim, the students select a random sample of size 100 and find a sample mean price of $52.80. Find the p-value and conduct a hypothesis test to determine if the price difference is significantly higher for α = 0.05.
- A certain chemical pollutant in the Genesee River has been constant for several years with mean μ = 34 ppm (parts per million) and standard deviation σ = 8 ppm. A group of factory representatives whose companies discharge liquids into the river is now claiming that they have lowered the average with improved filtration devices. A group of environmentalists will test to see if this is true. Assume their sample of size 50 gives a mean of 32.5 ppm. Find the p-value and perform a hypothesis test for α = 0.05.
- A manufacturing process produces ball bearings with diameters that have a normal distribution with known standard deviation of .04 centimeters. Ball bearings with diameters that are too small or too large are undesirable. Assume that a random sample of 25 gave a mean diameter of 0.51 centimeters. In order to test the claim that μ = 0.50 centimeters, find the p-value and perform a hypothesis test for α = 0.05.

Assignment:

- Follow election results Tue night
- Read analysis from fivethirtyeight.com