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 Duration A marine biologist claims that the mean dive duration of a harbor seal in Monterey Bay is at least 5.8 minutes. A random sample of 35 dive durations has a mean of 4.9 minutes and a standard deviation of 1.8 minutes. Is there enough evidence to reject the claim at $\alpha=0.01 ?$

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 Duration A marine biologist claims that the mean dive duration of a harbor seal in Monterey Bay is at least 5.8 minutes. A random sample of 35 dive durations has a mean of 4.9 minutes and a standard deviation of
1.8 minutes. Is there enough evidence to reject the claim at $\alpha=0.01 ?$

Key Concepts

Significance Level (?)

The significance level, typically denoted by ?, is a threshold set by the researcher to determine whether the observed data are statistically significant. It represents the risk level of making a Type I error (rejecting a true null hypothesis). If the P-value is below this threshold, the null hypothesis is rejected, indicating the observed effect is statistically significant.

P-Value

The P-value is a measure indicating the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. It provides a quantitative basis for decision making: a lower P-value suggests stronger evidence against the null hypothesis, leading to its rejection when compared to a predetermined significance level.

t-Test

The t-test is a statistical test used when the population standard deviation is unknown and the sample size is relatively small, assuming that the population is normally distributed. It involves calculating a test statistic that follows a t-distribution under the null hypothesis, which is then used to find the P-value to assess whether to reject the null hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves setting up two competing hypotheses, the null hypothesis (H0) which represents a default position or status quo, and the alternative hypothesis (Ha) which represents the research claim or a deviation from the status quo. Through the procedure, evidence against the null hypothesis is evaluated to determine if it should be rejected in favor of the alternative.

Null and Alternative Hypotheses

In hypothesis testing, the null hypothesis is a preliminary claim that there is no significant effect or difference, while the alternative hypothesis is the claim for which evidence is being sought. Setting these hypotheses correctly is crucial as they define the direction of the test, whether one-tailed or two-tailed, and help in interpreting the outcomes in relation to the research claim.

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