A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 107.6​, and the sample standard deviation is found to be 20.2.
Is the population mean greater than 100 at the α=0.025 level of​ significance?

-Determine the null and alternative hypotheses.
H0​:
Choices:
mu equals 100μ=100
mu less than 100μ<100
mu equals 100μ=100
mu greater than 100μ>100
mu less than 107.6μ<107.6
mu equals 107.6μ=107.6
mu greater than 107.6μ>107.6
H1​:
Choices:
mu greater than 100μ>100
mu less than 100μ<100
mu equals 100μ=100
mu greater than 100μ>100
mu less than 107.6μ<107.6
mu equals 107.6μ=107.6
mu greater than 107.6μ>107.6

-Compute the test statistic.
Choices:
t 0t0
t 0t0
z 0z0
=

-Determine the​ P-value.
The​ P-value is

-What is the result of the hypothesis​ test?
the null hypothesis because the​ P-value is the level of significance. At the α=0.025 level of​ significance, the population mean (is or is not)(greater than 100, less than 100 etc.)

Which is the graph of the piecewise function f(x)? f(x)=[tex]f(x) = \left \{ {{-x+1, x\leq 0 } \atop {x+1, x\ \textgreater \ 0}} \right.[/tex]

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.

You’re giving a cube with a length of 2.5 cm and a width of 2.5 cm and a high of 2.5 cm you place it on a scale and it is 295 g calculate the density