Hypothesis testing and inference Mathematics homework help

Don't use plagiarized sources. Get Your Custom Essay on

Hypothesis testing and inference Mathematics homework help

Just from $5/Page

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)

Child | Mean seconds of concentration in an experiment of reading | z-score( z = [X – µ]/σ) | p-value |

1 | 75 | –2.50 | 0.006 |

2 | 81 | –1.90 | 0.029 |

3 | 89 | –1.10 | 0.136 |

4 | 99 | –0.10 | 0.460 |

5 | 115 | 1.50 | 0.067 |

6 | 127 | 2.70 | 0.004 |

7 | 138 | 3.80 | <0.001 |

8 | 139 | 3.90 | <0.001 |

9 | 142 | 4.20 | <0.001 |

10 | 148 | 4.80 | <0.001 |

**Table 2** (µ = 100 seconds and σ = 20)

Child | Mean seconds of concentration in an experiment of reading | z-score( z = [X – µ]/σ) | p-value |

1 | 75 | –1.25 | 0.106 |

2 | 81 | –0.95 | 0.171 |

3 | 89 | –0.55 | 0.291 |

4 | 99 | –0.05 | 0.480 |

5 | 115 | 0.75 | 0.227 |

6 | 127 | 1.35 | 0.089 |

7 | 138 | 1.90 | 0.029 |

8 | 139 | 1.95 | 0.026 |

9 | 142 | 2.10 | 0.018 |

10 | 148 | 2.40 | 0.008 |

**Table 3** (µ = 100 seconds and σ = 30)

Child | Mean seconds of concentration in an experiment of reading | z-score | p-value |

1 | 75 | –0.83 | |

2 | 81 | –0.63 | |

3 | 89 | –0.37 | |

4 | 99 | –0.03 | |

5 | 115 | 0.50 | |

6 | 127 | 0.09 | |

7 | 138 | 1.27 | |

8 | 139 | 1.30 | |

9 | 142 | 1.40 | |

10 | 148 | 1.60 |

**Table 4** (µ = 100 seconds and σ = 40)

Child | Mean seconds of concentration in an experiment of reading | z-score | p-value |

1 | 75 | –0.63 | |

2 | 81 | –0.48 | |

3 | 89 | –0.28 | |

4 | 99 | –0.03 | |

5 | 115 | 0.38 | |

6 | 127 | 0.68 | |

7 | 138 | 0.95 | |

8 | 139 | 0.98 | |

9 | 142 | 1.05 | |

10 | 148 | 1.20 |

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 regions | Before vaccination | After vaccination |

1 | 85 | 11 |

2 | 77 | 5 |

3 | 110 | 14 |

4 | 65 | 12 |

5 | 81 | 10 |

6 | 70 | 7 |

7 | 74 | 8 |

8 | 84 | 11 |

9 | 90 | 9 |

10 | 95 | 8 |

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**

Year | Region 1 | Region 2 |

1 | 150 | 11 |

2 | 160 | 10 |

3 | 132 | 14 |

4 | 110 | 12 |

5 | 85 | 10 |

6 | 45 | 11 |

7 | 123 | 9 |

8 | 180 | 11 |

9 | 143 | 10 |

10 | 150 | 14 |

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 |

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more