Determine Whether The Hypothesis Is Left-Tailed Or Right-Tai

Determine whether the hypothesis is left tailed; right tailed; or two tailed. What parameter is being tested?

The null hypothesis presented is H₀: p = 0.76, and the alternative hypothesis is H₁: p > 0.76. Since H₁ specifies that the parameter p is greater than 0.76, the test is right-tailed. The parameter being tested in this hypothesis is the population proportion, p.

In hypothesis testing, the direction of the alternative hypothesis determines the tail of the test. A statement like H₁: p > 0.76 indicates a right-tailed test because it tests whether the population proportion is significantly greater than 0.76. Similarly, a hypothesis of the form H₁: p

Sample Paper For Above instruction

The determination of whether a hypothesis test is left-tailed, right-tailed, or two-tailed hinges upon the alternative hypothesis. In this case, the null hypothesis is H₀: p = 0.76, and the alternative hypothesis is H₁: p > 0.76. Since the alternative specifies that p is greater than 0.76, the test is right-tailed (Montgomery, 2017). The parameter being tested is the population proportion, p, which reflects the percent of the population sharing a particular characteristic. Hypothesis testing involves formulating hypotheses that specify the parameter value and the direction of deviation to assess statistical significance. A right-tailed test evaluates if the sample provides enough evidence to conclude that the population parameter exceeds a specified value. Recognizing the tail of the test assists in selecting the appropriate critical value and interpretation of results (Lehmann & Romano, 2005). Understanding the nature of the hypothesis ensures accurate inference about population parameters based on sample data.

In summary, the hypotheses suggest a right-tailed test for the population proportion p, with the parameter of interest being p. This classification guides the selection of critical values and the interpretation of the test statistic, ensuring proper statistical inference in evaluating whether the proportion exceeds 0.76 based on sample evidence.

References

• Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses (3rd ed.). Springer.
• Montgomery, D. C. (2017). Design and Analysis of Experiments. John Wiley & Sons.