## Essentials of Statistics (5th Edition)

$H_{0}:\mu=0.$ $H_{a}:\mu>0.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{3-0}{4.9/\sqrt{40}}=3.872.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=40-1=39, hence P is less than 0.01. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is less than $\alpha=0.05$, because it is less than 0.01, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the diet is effective.
The passage describes a hypothesis test, including the null and alternative hypotheses, the calculation of the test statistic, and the conclusion based on the P-value.
no_question

the text does not contain a mathematical question but rather provides a detailed explanation and conclusion of a statistical hypothesis test.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Essentials of Statistics (5th Edition)

$H_{0}:\mu=0.$ $H_{a}:\mu>0.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{3-0}{4.9/\sqrt{40}}=3.872.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=40-1=39, hence P is less than 0.01. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is less than $\alpha=0.05$, because it is less than 0.01, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the diet is effective.
user
The passage describes a hypothesis test, including the null and alternative hypotheses, the calculation of the test statistic, and the conclusion based on the P-value.

TYPE: NO_QUESTION

The text does not contain a mathematical question but rather provides a detailed explanation and conclusion of a statistical hypothesis test.