The graph below was drawn with output on the vertical axis and input on the horizontal axis. What does this graph indicate about the relationship between the input and the output?
A 10 by 10 grid on a coordinate plane is shown with a horizontal line graphed four units above the x-axis.
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Without a specific function or data points, it is difficult to infer the exact relationship between the input and output. However, we know that the output increases as the input increases because the line is above the x-axis. The slope of the line can give additional information about the rate of increase of the output with respect to the input.
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Mr. Moore is installing new work benches in the wood shop. He wants the height of the benches to be best for students standing and working on projects. He decides to use the mean height of the students in the school as a guide. The school has 6th, 7th, and 8th grade students. Rather than using the heights of all the students in the school, he decides to take a sample of students.
Suppose Mr. Moore decides to use 20 seventh graders as the sample. Is this sample a random sample? Explain your reasoning.
Mr. Moore decides to use a random number generator to select 20 students from the school. Suppose that when choosing 20 students using the random generator on the graphing calculator, Mr. Moore’s sample is all eighth graders. Does that mean the sample is not a random sample? Explain your reasoning.
A random sample is one where every member of the population has an equal chance of being selected for the sample.
In this case, Mr. Moore chose to only use 20 seventh-grade students as the sample. This does not necessarily mean that the sample is not random, but it may not be representative of the entire student population. If the seventh-grade students have different heights compared to the sixth and eighth-grade students, then the sample may not accurately represent the mean height of all students in the school.
However, if Mr. Moore used a random number generator to select the 20 students from all three grades, including sixth and eighth grades, then the sample can be considered a random sample.
If Mr. Moore's sample consisted of only eighth graders when using the random generator, then the sample may not be representative of the entire student population. This could be due to the small sample size or potential flaws in the random number generator. It is important to ensure that the sample is representative of the population when making decisions based on the sample data.
is there any way it can be in number form? or is that not possible?
Yes, it is possible to use numbers to explain the concept of a random sample. A random sample is one in which each member of a population has an equal and independent probability of being selected for the sample. This can be represented mathematically using probability theory.
For example, if a population has N members, and a simple random sample with size n is taken, then the probability of any particular member being selected for the sample is given by the formula:
P = n/N
Where P is the probability of selection, n is the sample size, and N is the population size.
If each member of the population has an equal chance of being selected, then the probability of selection is the same for all members:
P = 1/N
This ensures that the sample is free from bias and accurately represents the population.