Intro to Business Analytics

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One-sample z-test

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Intro to Business Analytics

Definition

A one-sample z-test is a statistical method used to determine whether the mean of a single sample is significantly different from a known population mean, under the assumption that the population variance is known. This test is commonly applied when the sample size is large (typically n > 30), allowing the sampling distribution of the sample mean to be approximated by a normal distribution, which makes it easier to calculate probabilities and make inferences about the population.

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5 Must Know Facts For Your Next Test

  1. The one-sample z-test calculates a z-score by taking the difference between the sample mean and the population mean, then dividing by the standard error of the sample mean.
  2. It requires that the sample is randomly selected and that the data points are independent from one another for valid results.
  3. The significance level (alpha) is set before conducting the test, typically at 0.05, which indicates a 5% risk of concluding that a difference exists when there is none.
  4. If the calculated z-score falls beyond the critical z-values determined by the significance level, you reject the null hypothesis.
  5. This test can be used in various fields such as psychology, business, and health sciences to make decisions based on sample data.

Review Questions

  • How does a one-sample z-test determine whether to reject or fail to reject the null hypothesis?
    • A one-sample z-test compares the calculated z-score from the sample data to critical z-values that correspond to a predetermined significance level. If the calculated z-score exceeds these critical values, it suggests that the sample mean is significantly different from the population mean, leading to rejection of the null hypothesis. This process involves checking if the observed difference is statistically significant based on established thresholds.
  • Discuss how assumptions of normality and independence impact the validity of results obtained from a one-sample z-test.
    • For a one-sample z-test to yield valid results, certain assumptions must be met. The data should be approximately normally distributed or have a large enough sample size for the Central Limit Theorem to apply. Additionally, each data point must be independent; if observations are related or dependent, it can skew results and lead to incorrect conclusions. Violating these assumptions can compromise the reliability of hypothesis testing outcomes.
  • Evaluate how understanding p-values from a one-sample z-test can aid decision-making in business analytics.
    • Understanding p-values derived from a one-sample z-test allows analysts to quantify the evidence against the null hypothesis in business contexts. A low p-value indicates strong evidence against it, suggesting that changes made within an organization could significantly impact performance metrics. This understanding enables businesses to make informed decisions regarding strategies or interventions based on statistical evidence rather than intuition alone, ultimately enhancing data-driven decision-making processes.
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