Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Write the null and alternative hypotheses for each of the following

Specifying the Null and Alternative Hypothesis

1) The t-test for independent samples,
2) One-way analysis of variance,
3) The t-test for correlation coefficients?,
4) The t-test for a regression coefficient.

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In each of these, the null hypothesis says there is no relationship and the alternative hypothesis says that there is a relationship.

  1. In this case the null hypothesis says that the two population means (i.e., $\mu_1$ and  $\mu_2$) are equal; the alternative hypothesis says that they are not equal.
  2. In this case the null hypothesis says that all of the population means are equal; the alternative hypothesis says that at least two of the means are not equal.
  3. In this case the null hypothesis says that the population correlation (i.e., $\rho$) is zero; the alternative hypothesis says that it is not equal to zero.
  4. In this case the null hypothesis says that the population regression coefficient ($\beta$) is zero, and the alternative says that it is not equal to zero.

The Author

Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.

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