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There are 122,100 public school teachers in Ohio and Ohio has a population of 11.6 million people. Illinois has a population of 12.9 million people. If the number of public school teachers per capita in Illinois was proportional to that of Ohio, how many public school teachers would we expect Illinois to have?
This problem uses proportionality or the relationship between two values. Typically, proportions are expressed as fractions. So, we can set this up as
and we can use this to express both of our values. So, for Ohio, we have
and for Illinois we have
. Now, because they are proportional, we can set them equal to each other and we get
. Now we can cross multiply to get
. To get the
alone on one side, we divide by
and we get 124,662.931034, which is about equal to 124,663.
Therefore, we expect Illinois to have 124,663 public school teachers
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the population proportion of gamers that prefer consoles is less than 28% as the manufacturer claims.
Of 341 surveyed players, 89 said that they prefer using a console.
The sample resulting sample proportion is p'= 89/341= 0.26
If the company claims is true then p<0.28, this will be the alternative hypothesis of the test.
H₀: p ≥ 0.28
H₁: p < 0.28
α: 0.05
To study the population proportion you have to use the approximation of the standard normal ≈N(0;1)
This test is one-tailed left, i.e. that you'll reject the null hypothesis to small values of Z, and so is the p-value, you can obtain it looking under the standard normal distribution for the probability of obtaining at most -0.82:
P(Z≤-0.82)= 0.206
Using the p-value approach:
If p-value ≤ α, reject the null hypothesis
If p-value > α, don't reject the null hypothesis
The decision is to not reject the null hypothesis.
Then at a level of 5%, you can conclude that the population proportion of gamers that prefer playing on consoles is at least 28%.
I hope this helps!