social stats homework

Social Statistics Takehome Assignment III: Inferential Statistics

In this section, we’ve learned two approaches to drawing inferences from samples to populations: parameter estimation (forming confidence intervals) and hypothesis testing (NHST). Use each approach to solve the 3 problems presented below. Note that for some problems is known (use z) and for some is estimated (use t).

1. For workers at an industrial plant, the historical mean level of production is 155 units produced per day, with a standard deviation of 15. Following the introduction of a new flextime worker option, a sample of 100 flextime workers produced and average of 160 units per day.

a) using the appropriate symbols, list the information provided by the problem

b) estimate the population mean of all flextime worker using the 95% confidence interval

c) test hypothesis that the flextime work option affets productivity by completing the following steps…

· Derive the null hypothesis.

· Find the critical value of the test statistic at the .05 level of significance.

· Calculate the value of the test statistic.

· State your conclusion.

· What decision error might your be committing?

1. Nationwide, the mean number of years that first-time drug offenders are sentenced is 12.16. A sample of 25 court records from your county indicates a mean number of years is 11.24, with a standard deviation of 3.11.

a) using the appropriate symbols, list the information provided by the problem

b) estimate the population mean of all drug offenders from your county using the 95% confidence interval

c) test hypothesis that first-time drug offenders in your county are treated differently than those nationally by completing the following steps…

· Derive the null hypothesis.

· Find the critical value of the test statistic at the .05 level of significance.

· Calculate the value of the test statistic.

· State your conclusion.

· What decision error might your be committing?

1. A standardized test, designed to measure students’ math skills has a mean score of 75 with a standard deviation of 10. As the principal of a private school, you’re curious how students in your school compare. A sample of 25 students from your school had a mean score of 79.

a) using the appropriate symbols, list the information provided by the problem

b) estimate the population mean of all students at your school using the 99% confidence interval.

c) test hypothesis that students at your school score differently than the national population by completing the following steps…

· Derive the null hypothesis.

· Find the critical value of the test statistic at the .01 level of significance.

· Calculate the value of the test statistic.

· State your conclusion.

· What decision error might your be committing?

Note: answer all questions in order and neatly. Show all work. No neat work, no credit. All work is to be original. Both parties involved in copied work will get ZEROs.