A statistics instructor believes that fewer than 20 % of...

A statistics instructor believes that fewer than $20 \%$ of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is a. at least $20 \%,$ when in fact, it is less than $20 \%$. b. $20 \%,$ when in fact, it is $20 \% .$ c. less than $20 \%,$ when in fact, it is at least $20 \%$ d. less than $20 \%,$ when in fact, it is less than $20 \% .$

A statistics instructor believes that fewer than $20 \%$ of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is
a. at least $20 \%,$ when in fact, it is less than $20 \%$.
b. $20 \%,$ when in fact, it is $20 \% .$
c. less than $20 \%,$ when in fact, it is at least $20 \%$
d. less than $20 \%,$ when in fact, it is less than $20 \% .$

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Key Concepts

Null and Alternative Hypotheses

The formulation of null and alternative hypotheses is central to the process of hypothesis testing. The null hypothesis represents the status quo or an accepted parameter value, while the alternative hypothesis reflects the specific claim or conjecture that the analysis seeks to support. Correctly defining these hypotheses is essential, as it frames the direction and criteria for statistical testing and error consideration.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. It involves formulating a null hypothesis, which assumes no effect or a specific value, and an alternative hypothesis, which represents the claim to be tested. By determining whether the data provide sufficient evidence to reject the null hypothesis, researchers can make informed conclusions about the validity of their assumptions.

Type I Error

A Type I error occurs when the null hypothesis is incorrectly rejected when it is actually true. This type of error leads to the conclusion that an effect or difference exists when, in reality, it does not. Controlling the probability of a Type I error is crucial in hypothesis testing and is typically managed by setting a significance level, which limits the risk of making such an incorrect inference.

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