(a) determine the null and alternative hypotheses, (b)...

(a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, and (c) explain what it would mean to make a Type II error. According to the Centers for Disease Control and Prevention, $16 \%$ of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of $6-$ to 11 -year-olds who are overweight is higher in her school district.

(a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, and (c) explain what it would mean to make a Type II error.
According to the Centers for Disease Control and Prevention, $16 \%$ of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of $6-$ to 11 -year-olds who are overweight is higher in her school district.

Key Concepts

Type I Error

A Type I error occurs when the null hypothesis is incorrectly rejected when it is actually true. This is analogous to a 'false positive' error, where one concludes that there is a significant effect or difference when none actually exists. The probability of committing a Type I error is denoted by the significance level (alpha) of the test.

Alternative Hypothesis

The alternative hypothesis represents a new claim or the effect that is being investigated, indicating that the parameter of interest deviates from the stated value in the null hypothesis. It is what the researcher believes might be true instead of the null hypothesis. In hypothesis testing, evidence is accumulated to determine whether there is enough support to reject the null hypothesis in favor of this alternative explanation.

Type II Error

A Type II error happens when the null hypothesis is not rejected when it is false, meaning that a real effect or difference goes undetected. This is known as a 'false negative' error. The probability of committing a Type II error is related to the test's power, which is the likelihood that the test correctly rejects a false null hypothesis.

Hypothesis Testing

Hypothesis testing is a fundamental technique in statistics used to make inferences about a population parameter based on sample data. It involves formulating two competing hypotheses – the null hypothesis, which represents the default or status quo assumption about the parameter, and the alternative hypothesis, which reflects the claim or research hypothesis that is being tested. Decisions to accept or reject the null hypothesis are made using statistical criteria, often based on the significance level of the test.

Null Hypothesis

The null hypothesis is a statement that there is no effect or no difference in the context of the study. It is the default assumption that any observed difference is due to sampling variability or random chance. In hypothesis testing, the null hypothesis is the claim that is tested against the observed data, and it is only rejected if there is strong statistical evidence to support the alternative hypothesis.

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