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Hypothesis Testing - Quantitative Techniques - Assignment, Exercises of Quantitative Techniques

University of AllahabadQuantitative Techniques

Hypothesis Testing, Test and Interpret, Null Hypotheses, Significance Level, Latah County, Individuals, Spent Outdoors, Randomly Sampled, Population, Sample Data are the key points of this assignment.

Typology: Exercises

2012/2013

Uploaded on 01/01/2013

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Quantitative Techniques in Sociology
Homework Assignment #7B: Hypothesis Testing (One-Sample)
Name: _________________________ Student ID#: _______________ Lab Time: _______
Complete the following questions on a separate sheet of paper. Be sure to: 1) show all of your work,
2) clearly label each problem, 3) put a box around your final answer, 4) use a pencil, 5) type
definitions, 6) present your work in a neat and orderly fashion, and 7) staple this cover sheet to your
other pages of completed work (do not paper-clip or fold). Remember, homework assignments are
designed to help you prepare for exams. The material covered within assignments will be very
similar to what appears on each test. Mastery of this material is crucial to pass this course. If you
cannot complete these problems by yourself, and in a reasonable amount of time, you will not be able
to pass the exam. If you are having troubles figuring out any of the material below see your lab
instructor immediately. Each item is worth up to 5 points; for a possible total of 85 points.
1) Define each of the following concepts in your own words. Give a complete and specific
definition and illustrate the concept by giving examples.
a) Hypothesis Testing
b) Τype II Error
c) α
2) Test and interpret the following null hypotheses, using an α = .05.
a) µ .50, ≥=x .54, s = .18, N = 22.
b) µ = 16, =x 14.1, s = 2.4, N = 160.
3) A random sample of 241 individuals is selected from Latah County. Their average
weekly amount of time spent outdoors is 18 hours with a standard deviation of 4.6 hours.
a) Using a significance level of .10, test and interpret the null hypothesis that µ = 25
hours.
b) Using a significance level of .01, test and interpret the null hypothesis that µ 20
hours. ≥
4) Twenty five counties are randomly sampled to test the research hypothesis that in the
population of all US counties the poverty rate is less than 120 per 10,000 population.
Construct, test, and interpret the null hypothesis using a ninety percent confidence level
and the following sample data: =x126, s = 24.
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Quantitative Techniques in Sociology Homework Assignment #7B: Hypothesis Testing (One-Sample)

Name: _________________________ Student ID#: _______________ Lab Time: _______

Complete the following questions on a separate sheet of paper. Be sure to: 1) show all of your work,

  1. clearly label each problem, 3) put a box around your final answer, 4) use a pencil, 5) type definitions, 6) present your work in a neat and orderly fashion, and 7) staple this cover sheet to your other pages of completed work (do not paper-clip or fold). Remember, homework assignments are designed to help you prepare for exams. The material covered within assignments will be very similar to what appears on each test. Mastery of this material is crucial to pass this course. If you cannot complete these problems by yourself, and in a reasonable amount of time, you will not be able to pass the exam. If you are having troubles figuring out any of the material below see your lab instructor immediately. Each item is worth up to 5 points; for a possible total of 85 points.

  2. Define each of the following concepts in your own words. Give a complete and specific definition and illustrate the concept by giving examples.

a) Hypothesis Testing

b) Τype II Error

c) α

  1. Test and interpret the following null hypotheses, using an α = .05.

a) μ ≥ .50, x = .54, s = .18, N = 22.

b) μ = 16, x =14.1, s = 2.4, N = 160.

  1. A random sample of 241 individuals is selected from Latah County. Their average weekly amount of time spent outdoors is 18 hours with a standard deviation of 4.6 hours.

a) Using a significance level of .10, test and interpret the null hypothesis that μ = 25 hours.

b) Using a significance level of .01, test and interpret the null hypothesis that μ 20 hours.

  1. Twenty five counties are randomly sampled to test the research hypothesis that in the population of all US counties the poverty rate is less than 120 per 10,000 population. Construct, test, and interpret the null hypothesis using a ninety percent confidence level and the following sample data: x =126, s = 24.

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  1. A researcher wants to be 95% sure that her theory is correct. Her theory is based on the hypothesis that on average the number of immigrants who illegally cross the US border of a small southwestern town has decreased over the last year. She conducts a study by collecting data from 12 different time periods (N=12) and concludes that the average number of individuals who cross the border during the present year is 394 with a standard deviation of 8. The official documents of the INS claim that the true average number of illegal immigrants, in the population of all illegal immigrants who crossed the board in this small town, last year was 399.

a) Compute and interpret the hypothesis test that the researcher would perform to answer her theoretical question.

b) What does the significance level tell us? That is, precisely what is it that has a probability of less than .05? Be specific.

  1. A researcher wants to test the null hypothesis that, in the population, the proportion of people who support capital punishment is equal to .36. In a sample of 146, 38% of the respondents believe in the death penalty. Test and interpret the null hypothesis using a .05 significance level.

  2. Computer Assignment 1 (be sure to attach a copy of your output) :*

a) Compute the mean for the variable hrs1 (number of hours worked per week). Test the null hypothesis that μ = 40.7 using a .05 significance level.

b) What is the research hypothesis?

c) Can we reject the null hypothesis? Explain why or why not.

  1. Computer Assignment 2 (be sure to attach a copy of your output) :*

a) Compute the proportion for the variable grass (should marijuana be made legal). Test the research hypothesis that the proportion of people who believe that marijuana should be made legal is not equal to 40% (π ≠ .40) using a. significance level.

b) What is the null hypothesis?

c) Do we find support for our research hypothesis? Explain why or why not.

  • Commands will be presented in lab.

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