In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). Although it remained slow, some politicians claimed that the recovery from the Great Recession was steady and noticeable. As a result, it was believed that the national percent of low-income working families was significantly lower in 2014 than it was in 2011. To support this belief, a spring 2014 sample of n=16 jurisdictions produced a sample mean of 29.8% for the percent of low-income working families, with a sample standard deviation of 4.1%. Using α=0.10 significance level, test the claim that the national average percent of low-income working families had improved by 2014.
1. Clearly restate the claim associated with this test, and state the null and alternate hypotheses.
2. Provide two or three sentences to state the type of test that should be performed based on the hypotheses. Additionally, state the assumptions and conditions that justify the appropriateness of the test.
3. Use technology to identify, and then provide the test statistic and the resulting P-value associated with the given sample results. Provide a statement that explains the interpretation of the P-value.
4. State, separately, both the decision/result of the hypothesis test, and the appropriate conclusion/statement about the claim.
(* I see this has been answered before on this website but I don't understand why a pooled variance was used to find the test statistic and P-value. Also, I would like to know how to find this using StatCrunch preferably.)
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In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). . .
Part 3: Hypothesis Testing In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). Although it remained slow, some politicians claimed that the recovery from the Great Recession was steady and noticeable. As a result, it was believed that the national percent of low-income working families was significantly lower in 2014 than it was in 2011. To support this...
During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a...
The Federal Pell Grant Program gives grants to low-income undergraduate students. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. We wonder if the mean amount is different this year for Pell grant recipients at San Jose State University. Suppose that we randomly select 50 Pell grant recipients from San Jose State University. For these 50 students, the mean Pell grant award is...
Location Percent Obesity Median Income Alabama 33.5 49,936 Alaska 29.7 68,734 Arizona 28.9 62,283 Arkansas 35.9 49,781 California 24.7 70,489 Colorado 21.3 73,034 Connecticut 26.3 72,812 Delaware 30.7 65,012 District of Columbia 21.7 85,750 Florida 26.2 54,644 Georgia 30.5 55,821 Hawaii 22.1 80,108 Idaho 28.9 58,728 Illinois 29.3 70,145 Indiana 32.7 59,892 Iowa 30.9 68,718 Kansas 31.3 63,938 Kentucky 31.6 54,555 Louisiana 34.9 49,973 Maine 28.2 58,663 Maryland 29.6 86,223 Massachusetts 23.3 86,345 Michigan 30.7 60,449 Minnesota 27.6 71,817 Mississippi...
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