Sec. 7.1 Introduction to Hypothesis Testing Mr. Ricks Madison High School

A hypothesis test uses sample statistics to test a claim about the value of a population parameter. A battery manufacturer claims that its AA batteries have a mean life of 300 minutes. How could we test this claim? How would we know if our results were meaningful? (That’s what this section is about)

2 Types of Hypotheses A null hypothesis (H0) contains a statement of equality, such as ≤, =, or ≥. The alternative hypothesis (HA) is the complement of the null hypothesis. It must be true if H0 is false, and it contains a statement of inequality, such as >, ≠, or <.

To write H0 and HA, translate the claim made about the population parameter into a mathematical statement and then write its complement. Here are some possible pairs of hypotheses for a parameter μ and a claim value k. 𝐻 0 :𝜇≤𝑘 𝐻 𝐴 :𝜇>𝑘 𝐻 0 :𝜇≥𝑘 𝐻 𝐴 :𝜇<𝑘 𝐻 0 :𝜇=𝑘 𝐻 𝐴 :𝜇≠𝑘

Write the claim as a mathematical sentence Write the claim as a mathematical sentence. State the null and alternative hypotheses, and identify which represents the claim. A water faucet manufacturer claims the mean flow rate for a certain type of faucet is less than 2.5 gallons per minute. A cereal company claims that the mean weight of the contents of its 20-ounce size cereal boxes is more than 20-ounces.

An automobile battery manufacturer claims that the mean life of a certain type of battery is 74 months. A university claims that the proportion of its students who graduate in four years is 82%. A radio station claims that its proportion of the local listening audience is greater than 39%.

When beginning a hypothesis test, we will assume the equality for the null hypothesis is true. Based on our sample, we will then… Reject the null hypothesis or Fail to reject the null hypothesis There is always the possibility that we are wrong because the only way to truly know whether H0 is true or false would be to test the entire population.

2 Types of Errors Exist Type I error – the null hypothesis is rejected when it is actually true Type II error – the null hypothesis is not rejected when it is actually false

The USDA limit for salmonella contamination for chicken is 20% The USDA limit for salmonella contamination for chicken is 20%. A meat packing company claims its chicken falls within the limit. You perform a hypothesis test to determine whether their claim is true. When will a type I or type II error occur? Which is more serious

A company specializing in parachute assembly claims its main parachute failure rate is not more than 1%. You perform a hypothesis test to determine if their claim is true. When will a type I or type II error occur? Which is more serious?

The level of significance is your maximum allowable probability of making a type I error and is denoted by α. 3 commonly used levels of significance are α = 0.10, α = 0.05, and α = 0.01. The probability of a type II error is denoted by β.

Review sample statistic vs Review sample statistic vs. population parameter A test statistic is a statistic that is compared to the parameter used in the null hypothesis Ex: if H0 involved μ, then our test statistic would be 𝑥

Assuming H0 is true, a P-value (or probability value) of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme or more extreme than the one determined from the sample data. The smaller the P-value computed from sample data, the stronger the evidence against H0.

Tailed-Tests The area in the tail is the P-value HA determines which tail to use Left-tailed (HA uses < symbol) Right-tailed (HA uses > symbol) Two-tailed (HA uses ≠ symbol)

Determine whether the hypothesis test for each is left-tailed, right-tailed, or two-tailed. A manufacturer of clocks claims the mean time its clocks lose is no more than 0.02 seconds per day The mean life of a certain tire is no less than 50,000 miles A research institute claims the mean length of most dreams is greater than 10 minutes

Hypothesis Test Decision Based on P-values If P ≤ α, then reject H0 If P > α, then fail to reject H0

Factors to Consider We do not accept H0, but rather we reject or fail to reject it (Why?) If HA is the claim then we can support the claim or fail to support the claim If you want to support a claim write it as HA If you want to reject a claim write it as H0

You represent a chemical company that is being sued for paint damage to automobiles. You believe the mean cost of repair per auto is about $650. From your point of view, how should you express your claim? You are on a research team that is investigating the mean temperature of adult humans. The commonly accepted claim is that the mean temperature is 98.6 ℉. From your point of view, how would this claim be best expressed?

Sec. 7.1 Pg. 331 #1-37 odd