8.5 practice - hypothesis testing proportions

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What is a null hypothesis (H0)?

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A null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default or starting assumption in hypothesis testing.

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What is an alternative hypothesis (Ha)?

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An alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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What does it mean to reject the null hypothesis?

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Rejecting the null hypothesis means that there is sufficient evidence to support the alternative hypothesis.

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What does it mean to fail to reject the null hypothesis?

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Failing to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis.

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What is a significance level (α)?

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The significance level (α) is the probability of rejecting the null hypothesis when it is actually true, commonly set at 0.05 or 0.01.

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How do you calculate the z-score in hypothesis testing?

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The z-score is calculated using the formula: z = (p̂ - p0) / sqrt[(p0(1 - p0)) / n], where p̂ is the sample proportion, p0 is the population proportion, and n is the sample size.

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What is a sample proportion (p̂)?

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A sample proportion (p̂) is the ratio of the number of successes in a sample to the total number of observations in that sample.

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What is the purpose of hypothesis testing?

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The purpose of hypothesis testing is to determine whether there is enough statistical evidence in a sample to infer that a certain condition holds true for the entire population.

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What does it mean if a z-score is negative?

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A negative z-score indicates that the sample proportion is less than the population proportion.

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What is the conclusion if the p-value is less than the significance level (α)?

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If the p-value is less than the significance level (α), you reject the null hypothesis.