WARM – UP As you prepare for College, one cost you should consider is your Meal Plan. A friend tells you that you should budget for $1000 in food cost per semester. You feel that the actual figure is something different. What can you conclude from an SRS of 10 universities? $1200 $1450 $1284 $920 $780 $1200 $1450 $1284 $920 $780 $1526 $1152 $1120 $1760 $1245 $1526 $1152 $1120 $1760 $1245 μ = The true mean cost of College Meal Plans per semester. H 0 : μ = 1000 H a : μ ≠ 1000 Since the P-Value is less than α = 0.05 the data IS significant. There is strong evidence to REJECT H 0. The average college meal plan is NOT $ SRS – Stated 2.Approximately Normal Distribution – Graph One Sample t – Test

In a Matched Pairs design subjects are matched in Homogeneous pairs or the same subject is used in both treatments. A common type is a Before-and-After Design. This leads to two Dependent data sets of which you subtract. MATCHED PAIRS t–TESTS Objective: Use the One sample t procedures to interpret a Matched Pairs t-test and be able to make inferences about the differences in the two treatments which share a common characteristic. CHAPTER 25

The Matched Pairs t-Procedures The Parameters and Statistics: μ d μ d = the true mean difference in the two populations. = the sample mean of all the differences of each individual pairing. = the sample standard deviation of all the differences H 0 : μ d = 0 H a : μ d ≠, 0 T-Test: 2.T-Test: Precede with a ONE SAMPLE t-Test for the mean difference with μ d always equal to Zero. Confidence Interval: 1.Confidence Interval: P-VALUES μ d <0: tcdf(-E99, t, df) μ d >0: tcdf(t, E99, df) μ d ≠0: 2·tcdf(|t|, E99, df)

EXAMPLE 1: Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test this, 10 cars are randomly selected. Each car is run using both regular and premium gas. The mileage is recorded. Is there sufficient evidence at the 0.05 level to support the belief? μ d = The true mean DIFFERENCE in gas mileage (Premium – Regular) H 0 : μ d = 0 H a : μ d > 0 Since the P-Value < α = REJECT H 0 STRONG evidence that Premium Gas does improve gas mileage. 1.SRS – Stated 2.Approximately Normal Distribution – Graph Car # Reg.Prem Prem. –Reg Matched Pairs 1-Sample t – Test

EXAMPLE 2: “Freshman – 15” Many people believe that students gain a significant amount of weight their freshman year of college. Is there enough evidence at the 5% level to support that there is a weight increase? Use the weights of 6 randomly chosen students. Student weights were measure at the beginning and at the end of the fall semester. μ d = The true mean DIFFERENCE in Weight in pounds (End of Semester – Beginning) H 0 : μ d = 0 H a : μ d > 0 Since the P-Value is NOT less than α = 0.05 Fail to REJECT H 0. The belief that Freshman experience weight increase `is not supported. 1.SRS – Stated 2.Approximately Normal Distribution – Graph BeginEnd End– Begin

EXAMPLE 3: The maker of a new tire claims that his Tires are superior in all road conditions. He claims that with his tires there is no difference in stopping distance between dry or wet pavement. To test this you select an SRS of 9 cars and at 60 mph you slam on the breaks. Estimate the Mean difference in stopping distance in feet with a 90% Confidence Interval. μ d = The true mean DIFFERENCE in stopping distance in feet (Wet – Dry Pavement) We are 90% Confident that the True mean difference in stopping distance in feet between Wet Pavement – Dry Pavement is between ft and ft. 1.SRS – Stated 2.Approximately Normal Distribution – Graph Car # WetDry Wet – Dry Dry Matched Pairs 1-Sample t – Interval

1000 Chips in Every Bag! 1000 Chips in Every Bag! Chips Ahoy used to advertise “1000 Chips in Every Bag!” 1.How would YOU do a significance test to test this? 2.What issues do you think would arise and how would you over come them?

1000 Chips in Every Bag! 1000 Chips in Every Bag! Chips Ahoy used to advertise “1000 Chips in Every Bag!” With 38 cookies in each bag, the true mean number of chips in each cookie should be 26.3 chips per cookie. Because there was a suspicion of LESS than 26.3 chip per cookie the company disregarded the ad. Test this claim by crumbling cookies and counting the number of chips in each. a.) Is there evidence to support the company’s decision. Gather evidence and Conduct a Significance test. b.) Estimate the true # of chips in the bag by finding a 95% Confidence Interval for the true # of chips per cookie and then multiply it by 38. c.) Eat your evidence.