SOLUTION: A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on th
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Question 921401: A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 130 people living in Gastown and finds that 24 have an annual income that is below the poverty line.
The government official will choose Gastown as a location for one of the social outreach programs if his sample data provide sufficient evidence to support that the true proportion of people living below poverty line is greater than 0.17. A test of hypothesis is conducted.
Part i) What is the null hypothesis?
Part ii) What is the alternative hypothesis?
I'm a little confused with proportions. I know that the alternative hypothesis is the "claim" that you are making, and the null is the opposite. So am I looking at the true proportion as the claim?
Would this be correct?
For Part i):
The true proportion of residents who are living below the poverty line is lower than 0.17.
For part ii):
The true proportion of residents who are living below the poverty line is greater than 0.17
You can put this solution on YOUR website! The null hypothesis ALWAYS has an equality in it in some way. This is so you get a fixed point to base the distribution model off of. You need to know this or else you'd have infinitely many distributions to choose from.
The claim is "the true proportion of people living below poverty line is greater than 0.17". If p is the population proportion, then the claim stated algebraically is .
The inequality does NOT have an "or equal to" part to it. Therefore, it is NOT part of the null hypothesis. This is the alternative hypothesis.
The null will be the remaining bit of the number line, ie the opposite of . The null is . Do not forget the "or equal to" part.
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