Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. the variance of road octane number for formulation 1 is
σ1^2=1.5
, and for formulation, 2 it is
σ2^2=1.2
two random samples of size
n1=15andn2=20
are tested, and the mean road octane numbers observed are
ẋ1=89.6
and
ẋ2=92.50
. assume normality.
a. if formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect it. formulate and test an appropriate hypothesis using α = 0.05. what is the p-value?
b. explain how the question in part (a) could be answered with a 95% confidence interval on the difference in mean road octane number.
c. what sample size would be required in each population if you wanted to be 95% confident that the error in estimating the difference in mean road octane number is less than 1?

Asphere has a diameter of 10 in. what is the volume of the sphere?

Find the cosine function that is represented in the graph.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.