Testing Claims Using P-Values (a) identify the claim and...

Testing Claims Using P-Values $(a)$ identify the claim and state $H_{0}$ and $H_{a}$, (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, and (d) interpret the decision in the context of the original claim. Assume the population is normally distributed. Dive Depth An oceanographer claims that the mean dive depth of a North Atlantic right whale is 115 meters. A random sample of 34 dive -depths has a mean of 121.2 meters and a standard deviation of 24.2 meters. Is there enough evidence to reject the claim at $\alpha=0.10 ?$ (Marine Ecology Progress Series)

Testing Claims Using P-Values $(a)$ identify the claim and state $H_{0}$ and $H_{a}$, (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, and (d) interpret the decision in the context of the original claim. Assume the population is normally distributed.
Dive Depth An oceanographer claims that the mean dive depth of a North Atlantic right whale is 115 meters. A random sample of 34 dive
-depths has a mean of 121.2 meters and a standard deviation of 24.2 meters. Is there enough evidence to reject the claim at $\alpha=0.10 ?$ (Marine Ecology Progress Series)

Key Concepts

Null Hypothesis (H0)

This is the statement of no effect or no difference that forms the basis of the hypothesis test. It typically asserts that the population parameter is equal to a specified value. Formulating the null hypothesis is the starting point in statistical inference, and it is what the test seeks to challenge using the data.

Alternative Hypothesis (Ha)

This hypothesis represents the claim that challenges the status quo represented by the null hypothesis. It asserts that the population parameter has a value different from, greater than, or less than the specified value. The alternative hypothesis reflects what the researcher is trying to prove or detect and guides the direction of the test.

P-value

The P-value is the probability of observing a test statistic at least as extreme as the one computed from the sample, assuming the null hypothesis is true. It quantifies the evidence against the null hypothesis. A smaller P-value indicates stronger evidence against H0, helping to determine whether to reject or not reject the null hypothesis.

Significance Level (?)

The significance level is the threshold probability used to decide whether to reject the null hypothesis. It represents the maximum risk of committing a Type I error (rejecting a true null hypothesis) that the researcher is willing to accept. Comparing the P-value to ? helps in making the decision in the hypothesis test.

Test Statistic

The test statistic is a standardized value calculated from sample data during a hypothesis test. It measures how far the sample statistic deviates from the value specified in the null hypothesis, in units of the standard error. When the population standard deviation is unknown and the sample size is small, a t-test is often used to compute the test statistic.

Decision Making in Hypothesis Testing

This concept involves using the computed P-value and comparing it to the significance level to decide whether to reject the null hypothesis. If the P-value is less than the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. This decision is then interpreted in the context of the original claim, assessing the strength of evidence against the null hypothesis.

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