Purchase Solution

P-value, test statistic, level of significance and critical value

Not what you're looking for?

Ask Custom Question

Prepare a three-paragraph discussion of the relationship between p-value, test statistic, level of significance, and critical value. Allot one paragraph for each term. Discuss p-values for two sided and one-sided tests. Provide an example for tests using Z, Student-t, and Chi-squared. Provide equations for each when possible and discuss how these terms help with hypothesis decisions.

Purchase this Solution
Solution Summary

P-value, test statistic, level of significance and critical value are discussed. Equations are provided to discuss hypothesis decisions.

Solution Preview

The p-value approach is a recent development in hypothesis testing procedure when it has become much easier to calculate exact probabilities using computer software such as MS Excel, SPSS, SAS, Megastat etc. p-value is the probability of obtaining a value of the test statistic as extreme as the one calculated under the assumption that the null hypothesis is true. If p-value is less than the level of significance, the null hypothesis is rejected, no matter whether it is a left-tailed or right-tailed or two tailed test. Normally, the default level of significance (which is also called the probability of committing a Type I error) is 0.05, and the decision rule in the hypothesis testing process is to reject the null hypothesis if p-value is less than 0.05.
The test statistic is the value calculated using the sample data, namely, the mean, the standard deviation and the sample size. If the test statistic value comes out to be larger than the critical value in a right-tailed test or smaller than the critical value in a left-tailed test, the null hypothesis is rejected. If the absolute value of the test statistic is larger than the critical value in a two-tailed test, the null hypothesis is rejected again.
The level if significance, also called the probability of Type I error, is a fraction or percentage which demarcates the acceptance ...

Purchase this Solution
Free BrainMass Quizzes
Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

View More Free Quizzes
Related BrainMass Solutions

  • Relationship among p-value, significance level, and critical

    241069 Relationship Among P-Value, Significance Level, Critical Value What is the relationship among p-value, significance level, and critical value? See the attached Word document.

  • Finding statistic, critical value and p value: Example problem

    214936 Finding statistic, critical value and p value: Example problem Suppose a study is constructed to test a claim, at a 0.05 significance level that a population proportion is 40%.

  • Hypothesis Testing Using Normal Distribution

    0.054067524 Do not reject the null hypothesis Find the critical value(s) for the t-test with the indicated sample size n and level of significance a.

  • Testing of hypothesis: Students t test

    Rejection criteria: Reject the null hypothesis, if the test statistic is less than the critical value of t with 63 d.f at 0.03 significance level. The test Statistic is given by c. What is the value of the test statistic?

  • Hypothesis test: sample of 100

    Answer The test Statistic is given by Z = (X - u)/(sigma/sqrt(n)) = (X - 80)/(12/sqrt(100)) Significance level = 0.01 Decision rule : Reject the null hypothesis if the p value is less than the significance level.

  • Hypothesis Testing of Proportion

    Statistic 1.902175669 Upper-Tail Test Upper Critical Value 1.644853627 p-Value 0.028574096 Reject the null hypothesis When significance level, α = 1% The null hypothesis tested is H0: The proportion of freshmen had at least one A in

  • Test of hypothesis

    158583 Find the test statistic, p-value and critical value and state a final conclusion Find the test statistic, p-value and critical value and state a final conclusion.

  • t-test

    Find the null and alternative hypotheses, test statistic, P-value (or range of P-values), critical value(s), and state the final conclusion. Claim: The mean life span of desktop PCs is less than 7 years.

  • Hypothesis Testing of Mean & Proportion

    Z Test Statistic -3.572175839 Two-Tail Test Lower Critical Value -2.58 Upper Critical value 2.58 p-Value 0.000354028 Reject the null hypothesis 8.

  • Using the "Traditional" and "P-Value" Method for Hypotheses

    value of test statistic is greater than the critical value at the 0.05 significance level.

View More Related Solutions