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.

12. Clearly restate the claim associated with this test, and state the null and alternate hypotheses.
13. 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.
14. 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. (Print or copy-and-paste the output that identified these values, or any other form of evidence that technology was used.)
15. State, separately, both the decision/result of the hypothesis test, and the appropriate conclusion/statement about the claim.

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. State, separately, both the decision/result of the hypothesis test, and the appropriate conclusion/statement about the claim.

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. (Print or copy-and-paste the output that identified these values, or any other form of evidence that technology was used.)
4. State, separately, both the decision/result of the hypothesis test, and the appropriate conclusion/statement about the claim.

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.

I looked at the solutions when I searched this question up but I was confused as to why the solutions used z test instead of t test, shouldn’t that be used when the sample size is larger than 30? I’m also confused on why the alternative hypothesis is mu more than 31.3 instead of less than symbol? Thanks in advance!!