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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblema 7.T.4
Capitolo 7, Problema 7.T.4

A research center claims that more than 80% of U.S. adults think that mothers should have paid maternity leave. In a random sample of 50 U.S. adults, 82% think that mothers should have paid maternity leave. At α=0.05, is there enough evidence to support the center’s claim?

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Step 1: Define the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis is H₀: p ≤ 0.80 (the proportion of U.S. adults who think mothers should have paid maternity leave is 80% or less). The alternative hypothesis is Hₐ: p > 0.80 (the proportion is greater than 80%).
Step 2: Identify the sample proportion (p̂), the sample size (n), and the significance level (α). Here, p̂ = 0.82, n = 50, and α = 0.05.
Step 3: Calculate the test statistic using the formula for a one-sample z-test for proportions: z = (p̂ - p₀) / √((p₀(1 - p₀)) / n), where p₀ is the hypothesized population proportion (0.80).
Step 4: Determine the critical value for a one-tailed test at α = 0.05. Use a z-table or statistical software to find the z-critical value corresponding to a right-tailed test.
Step 5: Compare the calculated z-test statistic to the critical value. If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Interpret the result in the context of the research center's claim.

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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1). In this case, the null hypothesis would state that 80% or fewer U.S. adults support paid maternity leave, while the alternative hypothesis would assert that more than 80% do. The goal is to determine if the sample data provides sufficient evidence to reject the null hypothesis.
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06:21
Step 1: Write Hypotheses

P-Value

The p-value is a measure that helps determine the significance of the results obtained from a hypothesis test. It represents the probability of observing the sample data, or something more extreme, assuming the null hypothesis is true. If the p-value is less than the significance level (α), typically set at 0.05, it indicates strong evidence against the null hypothesis, leading to its rejection in favor of the alternative hypothesis.
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06:50
Step 3: Get P-Value

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter. In this context, it can provide insight into the proportion of U.S. adults who support paid maternity leave. By calculating a confidence interval for the sample proportion, researchers can assess whether the interval includes the hypothesized value of 0.80, which would affect the conclusion of the hypothesis test.
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Introduction to Confidence Intervals
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