Job Search A Gallup poll of 195,600 employees showed that 51% of them were actively searching for new jobs. Use a 0.01 significance level to test the claim that the majority of employees are searching for new jobs

검증된 단계별 안내

Formulate the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis is H₀: p ≤ 0.5 (the proportion of employees actively searching for new jobs is 50% or less). The alternative hypothesis is Hₐ: p > 0.5 (the proportion of employees actively searching for new jobs is greater than 50%).

Identify the significance level (α). The problem specifies a significance level of 0.01, which means there is a 1% risk of rejecting the null hypothesis when it is true.

Calculate the test statistic using the formula for a one-proportion z-test: z = (p̂ - p₀) / √((p₀(1 - p₀)) / n), where p̂ is the sample proportion (0.51), p₀ is the hypothesized proportion (0.5), and n is the sample size (195,600).

Determine the critical value for a one-tailed z-test at the 0.01 significance level. Use a z-table or statistical software to find the z-value corresponding to a cumulative probability of 0.99.

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 problem.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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, H0 would state that 50% or fewer employees are searching for new jobs, while H1 would claim that more than 50% are. The test assesses whether the sample data provides enough evidence to reject H0 in favor of H1.

Significance Level

The significance level, denoted as alpha (α), is the threshold for determining whether to reject the null hypothesis. A significance level of 0.01 indicates a 1% risk of concluding that a difference exists when there is none (Type I error). In this scenario, it means that the results must be statistically significant at the 1% level to support the claim that the majority of employees are job searching.

P-Value

The p-value is a statistic that helps determine the strength of the evidence against the null hypothesis. It represents the probability of observing the sample data, or something more extreme, if the null hypothesis is true. If the p-value is less than the significance level (0.01 in this case), it suggests that the observed data is unlikely under H0, leading to its rejection and supporting the claim that the majority of employees are searching for new jobs.