High School

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For the following data from an experiment, test the hypothesis that [tex]H_0: M = 1.4[/tex] versus [tex]H_A: M > 1.4[/tex] at [tex]\alpha = 0.05[/tex].

Data: 1.51, 1.35, 1.69, 1.48, 1.29, 1.27, 1.54, 1.39, 1.45

Answer :

Final answer:

The student is asking about hypothesis testing in statistics. They wish to test a null hypothesis against an alternative hypothesis at a certain significance level. The correct way to do this is by calculating the sample mean and standard deviation, formulating the hypotheses, and then conducting a one-sample t-test.

Explanation:

The subject of this question is hypothesis testing in statistics. This is a method used to make inferences or draw conclusions about a population based on a sample of data. The student wants to test the null hypothesis H0: M = 1.4 against the alternative hypothesis HA: M >1.4 at a significance level α = 0.05.

Here is how you can proceed: First, calculate the sample mean (M) and standard deviation (σ) from the given data. Next, formulate the null and alternative hypotheses. In this case, the null hypothesis (H0) is that the mean (M) is equal to 1.4, and the alternative hypothesis (HA) is that the mean (M) is greater than 1.4. Next, perform a one-sample t-test using a significance level of 0.05 (α = 0.05). The result of the t-test will tell you whether to reject or fail to reject the null hypothesis.

In conclusion, it is critical to understand the statistical concepts involved in hypothesis testing, the formulation of null and alternative hypotheses, and the correct interpretation of the test result in order to make accurate inferences about the population.

Learn more about Hypothesis Testing here:

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