Chapter 9Hypothesis Testing

9.2

Testing a Hypothesis about ,

Known

THREE WAYS TO STRUCTURE THE HYPOTHESIS TEST:

Let’s revisit the researcher who believes that the mean length of a cell phone call has increased from its June, 2001 mean of 2.62 minutes. What is the null and alternative hypothesis?

We will assume the length of the phone call is still 2.62 minutes. Suppose we take a simple random sample of 36 cell phone calls. Assume the standard deviation length of a phone call is known to be 0.78 minutes. What is the sampling distribution of the sample mean?.

We will reject the null hypothesis if the sample mean is “too far” from the assumed population mean. What does this mean?

We might define “too far” as too many standard deviations from the assumed population mean

For example, we might reject the null hypothesis if the sample mean is more than 2 standard deviations above the population mean. Why?

z 0 1 2

Area = 0.0228

If the null hypothesis is true, then 1 - 0.0228 = 0.9772 = 97.72% of all sample means will be less than

Because sample means greater than 2.88 are unusual if the population mean is 2.62, we are inclined to believe the population mean is greater than 2.62.

Step 1: A claim is made regarding the population mean. The claim is used to determine the null and alternative hypotheses. Again, the hypothesis can be structured in one of three ways:

The critical region or rejection region is the set of all values such that the null hypothesis is rejected.

Step 4: Compare the critical value with the test statistic:

Step 5: State the conclusion.

EXAMPLE The Classical Method of Hypothesis Testing

A can of 7-Up states that the contents of the can are 355 ml. A quality control engineer is worried that the filling machine is miscalibrated. In other words, she wants to make sure the machine is not under- or over-filling the cans. She randomly selects 9 cans of 7-Up and measures the contents. She obtains the following data. 351 360 358 356 359

358 355 361 352

EXAMPLE The Classical Method of Hypothesis Testing

A P-value is the probability of observing a sample statistic as extreme or more extreme than the one observed under the assumption the null hypothesis is true.

Hypothesis Test Regarding μ with σ Known (P-values)

Step 1: A claim is made regarding the population mean. The claim is used to determine the null and alternative hypotheses. Again, the hypothesis can be structured in one of three ways:

Step 3: Compute the P-value.

EXAMPLE Testing a Hypothesis Testing Using P-values

EXAMPLE Testing a Hypothesis Using P-values

A can of 7-Up states that the contents of the can are 355 ml. A quality control engineer is worried that the filling machine is miscalibrated. In other words, she wants to make sure the machine is not under- or over-filling the cans. She randomly selects 9 cans of 7-Up and measures the contents. She obtains the following data. 351 360 358 356 359

358 355 361 352