Warm Up Yvon Hopps ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high quality popcorn with less than 10% of the kernels left unpopped, on average. After experimenting with several bags, he determined that power 9 at 4 minutes was the best combination.

Warm Up Continue To be sure his method was successful, he popped 8 more bags of popcorn at random at this setting. All were of high quality with the following percentages of uncooked popcorn: 7, 13.2, 10, 6, 7.8, 2.8, 2.2, 5.2. Does this provide evidence that he met his goal of an average of no more than 10% uncooked kernels?

Inference for Comparing Two Means Part VI – Learning about the World Inference for Comparing Two Means

A construction manager thinks that being a construction worker is more stressful than being a corporate CEO. He decides to measure blood pressure to test this theory. 20 randomly selected construction workers have an average systolic blood pressure of 134 mmHg with a standard deviation of 13 mmHg. 25 randomly selected CEOs have an average blood pressure of 122 mmHg with a standard deviation of 8 mmHg. Does this data support the construction manager’s claim?

Hypotheses μ1= the average blood pressure for all construction workers μ2 = the average blood pressure for all CEOs H0: μ1= μ2 Ha: μ1> μ2

Type of Test Right-tailed two sample t-test α = .05 df = 19 (use the smaller of the two values when you do this by hand; your calculator will use a different value)

Conditions Data must come from two independent random samples Two treatment groups in a randomized experiment are also acceptable Each sample is < 10% of the population Both populations should be approximately normal or the samples should be large (same robustness as single sample t with same ranges for n)

In this problem… Condition Check Random Samples Independent Groups Each n < 10%N Both populations approx. normal or large samples Stated Assume (nothing in problem indicates the two are related) There are more than 200 construction workers and 250 CEOs Assume no outliers or strong skew in either set of sample data

Finding t… USE YOUR FORMULA SHEET

Finding t…

In this problem…

The Rest of the Problem… Find the p-value: Since p < .05, reject H0. There is enough evidence to conclude that average blood pressure is higher for construction workers than for CEOs.

Confidence Intervals Find a 96% confidence interval for the difference in the mean blood pressures of the two groups.

Confidence Intervals We are 96% confident that the difference between the true mean blood pressure of construction workers and that of CEOs is between 4.7 mmHg and 19.3 mmHg.

Using your calculator Your calculator uses a less conservative estimate for df Both answers are right, just make sure you list the degrees of freedom that you are actually using

Homework 24-1 p. 579 #12, 13, 29, 36