Write the null and alternative hypotheses you would use to...

Write the null and alternative hypotheses you would use to test each of the following situations: a) A president is concerned about his "positives"- the percentage of the country's residents who express approval of his job performance. His political committee pays for a series of TV ads, hoping that they can keep the positives above $65 \%$. They will use follow-up polling to assess the ads' effectiveness. b) In the 1980 s only about $13 \%$ of the population attained a bachelor's degree. Has the percentage changed? c) Only about $27 \%$ of people who try to earn money succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people succeed.

Write the null and alternative hypotheses you would use to test each of the following situations:
a) A president is concerned about his "positives"- the percentage of the country's residents who express approval of his job performance. His political committee pays for a series of TV ads, hoping that they can keep the positives above $65 \%$. They will use follow-up polling to assess the ads' effectiveness.
b) In the 1980 s only about $13 \%$ of the population attained a bachelor's degree. Has the percentage changed?
c) Only about $27 \%$ of people who try to earn money succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people succeed.

Key Concepts

Null Hypothesis

The null hypothesis is a default statement that there is no effect or no difference between a population parameter and a specified value, or between two groups under comparison. It serves as a starting point for statistical testing and is presumed true until evidence suggests otherwise.

Alternative Hypothesis

The alternative hypothesis is a statement that contradicts the null hypothesis by asserting that there is an effect, a difference, or a deviation from a specified value. It represents what a researcher aims to support with evidence through data analysis.

One-Tailed Test

A one-tailed test is used when the research hypothesis predicts the direction of an effect or difference (e.g., greater than or less than a certain value). This type of test assesses the probability of a statistic falling in one specific tail of the probability distribution.

Two-Tailed Test

A two-tailed test is used when the research hypothesis does not predict the direction of the effect, simply stating that there is a difference from a specific value. In this case, the test evaluates the probability of the statistic falling in either tail of the distribution, capturing deviations on both sides.

Population Proportion Testing

Population proportion testing is a statistical method used to evaluate hypotheses about the proportion of individuals in a defined population that possess a particular characteristic. It involves comparing a sample proportion to a hypothesized value, which is crucial when assessing claims related to percentages or rates in the population.

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