Hypothesis Testing and Inference

profiledabmnash

 

 

This assignment focuses on estimation and hypothesis testing with one-sample and two-sample inferences.

The essence of parametric testing is the use of standard normal distribution tables of probabilities. For each exercise, there will be a sample problem that shows how the calculations are done and at least one problem for you to work out.

For the first assignment, you will not need any statistical software. However, you will use a standardized normal distribution table (a z-score table) provided in the course textbook (Table 3—The normal distribution—in the Tables section in APPENDIX) to obtain your responses.

Click here to access the standardized normal distribution table from your course textbook. (Attached)

 

Problem 1: Probability Using Standard Variable z and Normal Distribution Tables

Variables are the things we measure. A hypothesis is a prediction about the relationship between variables. Variables make up the words in a hypothesis.

In the attention-deficit/hyperactivity disorder's (ADHD's) hypothetical example provided in the tables below, the research question was, What is the most effective therapy for ADHD? One of the variables is type of therapy. Another variable is change in ADHD-related behavior, given exposure to therapy. You might measure change in the mean seconds of concentration time when children read. This experiment is designed to obtain children's concentration times while they read a science textbook and to find out whether the therapy used worked on any of the children.

Use the stated µ and σ to calculate probabilities of the standard variable z to get the value of p (up to three decimal places). In addition, respond to the following questions for each pair of parameters:

  • Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?
  • What happens to the "significance" of each child's data as the data are progressively more dispersed?

In addition to the above, write a formal statement of conclusion for each child in APA style. A report template is provided for submission of your work. (Attached)

Note: Tables 1 and 2 are practice tables with answers. Tables 3 and 4 are the assignment tables for you to work on.

Table 1 (µ = 100 seconds and σ = 10)

ChildMean seconds of concentration in an experiment of readingz-score
(z = [X – µ]/σ)
p-value
175–2.500.006
281–1.900.029
389–1.100.136
499–0.100.460
51151.500.067
61272.700.004
71383.80<0.001
81393.90<0.001
91424.20<0.001
101484.80<0.001

Table 2 (µ = 100 seconds and σ = 20)

ChildMean seconds of concentration in an experiment of readingz-score
(z = [X – µ]/σ)
p-value
175–1.250.106
281–0.950.171
389–0.550.291
499–0.050.480
51150.750.227
61271.350.089
71381.900.029
81391.950.026
91422.100.018
101482.400.008

Table 3 (µ = 100 seconds and σ = 30)

ChildMean seconds of concentration in an experiment of readingz-scorep-value
175–0.83 
281–0.63 
389–0.37 
499–0.03 
51150.50 
61270.09 
71381.27 
81391.30 
91421.40 
101481.60 

Table 4 (µ = 100 seconds and σ = 40)

ChildMean seconds of concentration in an experiment of readingz-scorep-value
175–0.63 
281–0.48 
389–0.28 
499–0.03 
51150.38 
61270.68 
71380.95 
81390.98 
91421.05 
101481.20 

Click here for a template to provide your answers and submit the assignment. (Attached)

 

Problem 2: Two-Sample Inferences

A two-sample inference deals with dependent and independent inferences. In a two-sample hypothesis testing problem, underlying parameters of two different populations are compared.

In a longitudinal (or follow-up) study, the same group of people is followed over time. Two samples are said to be paired when each data point in the first sample is matched and related to a unique data point in the second sample.

This problem demonstrates inference from two dependent (follow-up) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in sub-Saharan Africa. Conclusion about the null hypothesis is to note the difference between samples.

The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination.

Table 5: Cases of TB in Different Geographical Regions

Geographical regionsBefore vaccinationAfter vaccination
18511
2775
311014
46512
58110
6707
7748
88411
9909
10958

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:

  • Construct a one-sided 95% confidence interval for the true difference in population means.
  • Test the null hypothesis that the population means are identical at the 0.05 level of significance.

In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.

 

Problem 3: Cross-Sectional Study

In a cross-sectional study, the participants are seen at only one point of time. Two samples are said to be independent when the data points in one sample are unrelated to the data points in the second sample.

The problem that demonstrates inference from two independent samples will use hypothetical data from the American Association of Poison Control Centers.

There are two groups of independent data collected in different regions, which also calls for a t-test. The numbers represent the number of recorded cases of poisoning with chemicals in the homes of 100,000 people in two regions.

Table 6: Cases of Poisoning With Chemicals

YearRegion 1Region 2
115011
216010
313214
411012
58510
64511
71239
818011
914310
1015014

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:

  • Formulate a null and an alternative hypothesis for a two-sided test.
  • Conduct the test at the 0.05 level of significance.

In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.

Submit your Minitab output file and document separately

Assignment 3 Grading Criteria
Maximum Points
Initial setup of the assignment—introduction.
10
Accuracy of the z-scores.
20
Accuracy of the p-values.
20
Proper use of the Minitab statistical analysis tool and execution.
10
Provided a copy of the output.
10
Written interpretation of results using correct spelling, grammar, professional vocabulary, and APA format.
30
Total:
100

 

  • 7 years ago
  • 20
Answer(1)

Purchase the answer to view it

blurred-text
NOT RATED
  • attachment
    hypothesis_testing.xlsx
  • attachment
    hypothesis_testing.docx
Bids(1)