You flip a coin and record whether it shows heads or tails....

You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is $50 \%,$ but you think it is less for this particular coin. What type of test would you use?

Key Concepts

Proportion Test

A proportion test is a statistical method used to compare an observed sample proportion to a hypothesized population proportion. When dealing with binary outcomes, this test helps determine if the observed deviation from the expected proportion is statistically significant, often using either a binomial test or a z-test under certain conditions.

Binomial Distribution

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. It is particularly relevant for experiments with two outcomes, such as coin flips, where each flip is independent and has the same chance of resulting in one of the two outcomes.

Hypothesis Testing

Hypothesis testing involves making an assumption (the null hypothesis) about a population parameter and then using sample data to decide whether to reject that assumption. It provides a framework to determine if observed data deviates significantly from what was expected under the assumption, using statistical evidence rather than guesswork.

One-Tailed Test

A one-tailed test is used when the alternative hypothesis specifies a direction of the effect, such as testing whether a parameter is less than or greater than a certain value. This approach focuses solely on one end of the probability distribution, thereby increasing the test's power to detect an effect in that specific direction.

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