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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 7.4.4
Capitolo 7, Problema 7.4.4

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.
Claim: p ≥0.48, α=0.08. Sample statistics: p_hat = 0.40, n=90

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Step 1: Verify the conditions for using a normal sampling distribution. The two conditions are: (1) The sample size n must be large enough such that both n * p and n * (1 - p) are greater than or equal to 5, and (2) the sampling must be random and independent.
Step 2: Calculate n * p and n * (1 - p) using the claimed population proportion p = 0.48 and sample size n = 90. Use the formulas: n * p and n * (1 - p).
Step 3: Check if both n * p and n * (1 - p) are greater than or equal to 5. If they are, then the normal approximation can be used. If not, the normal approximation cannot be used.
Step 4: If the normal approximation is valid, calculate the test statistic z using the formula: z = (p̂ - p) / sqrt((p * (1 - p)) / n), where p̂ is the sample proportion, p is the claimed proportion, and n is the sample size.
Step 5: Compare the calculated z-value to the critical z-value for the given significance level α = 0.08 in a one-tailed test. Determine whether to reject or fail to reject the null hypothesis based on this comparison.

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Normal Sampling Distribution

A normal sampling distribution is applicable when the sample size is sufficiently large, typically n ≥ 30, and the population proportion is not too close to 0 or 1. This allows the sampling distribution of the sample proportion (p_hat) to be approximated by a normal distribution, facilitating hypothesis testing and confidence interval estimation.
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Sampling Distribution of Sample Proportion

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample statistics to determine whether to reject H0 in favor of H1, based on a predetermined significance level (α).
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Step 1: Write Hypotheses

Sample Proportion (p_hat)

The sample proportion (p_hat) is the ratio of the number of successes in a sample to the total number of observations in that sample. It serves as an estimate of the population proportion (p) and is crucial for conducting hypothesis tests regarding population proportions, especially when comparing it to a claimed value.
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Sampling Distribution of Sample Proportion
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