Assignment 2: Conducting A Z-Test Researcher Predicts That W

Assignment 2 Conducting A Z Testa Researcher Predicts That Watching A

Determine whether watching a film about institutionalization significantly changes students' attitudes towards chronically mentally ill patients using a z-test. The sample consists of 36 students with a mean attitude score of 70. The general population mean score is 75 with a standard deviation of 12. Conduct the five steps of hypothesis testing at a 5% significance level to assess if the film influences attitudes.

Explain what it means to set alpha at .05. State the null and alternative hypotheses, specify whether the test is one-tailed or two-tailed, identify the critical z-value, calculate the obtained z-score, and interpret whether to reject or fail to reject the null hypothesis. Clarify your findings in words, emphasizing the significance of the results.

Paper For Above instruction

In the realm of statistical hypothesis testing, setting a significance level (alpha) at 0.05 is a standard practice that delineates the threshold for determining statistical significance. Essentially, alpha represents the probability of committing a Type I error, which is erroneously rejecting the null hypothesis when it is, in fact, true. By selecting a 0.05 level, researchers accept a 5% chance of falsely declaring an effect or difference when none exists. This threshold balances the need for sensitivity to detect effects and the risk of false positives, thereby guiding the interpretation of p-values derived from statistical tests.

The null hypothesis (H₀) asserts that the film has no effect on students’ attitudes towards the chronically mentally ill; that is, the mean attitude score after watching the film is equal to the general population mean. Mathematically, this is expressed as H₀: μ = 75. Conversely, the alternative hypothesis (H₁) posits that the film influences attitudes, leading to a deviation from the population mean. Since the researcher predicts that attitudes will change in either direction (more positive or more negative), this is a two-tailed hypothesis: H₁: μ ≠ 75.

Given the nature of the hypothesis, we identify it as a two-tailed test, which considers deviations in both directions from the population mean. For a two-tailed test at an alpha of 0.05, the critical z-values are approximately ±1.96. These critical values mark the boundaries beyond which the null hypothesis will be rejected, indicating statistically significant differences from the population mean.

The sample mean (M) is 70, with a sample size (n) of 36, population mean (μ₀) of 75, and population standard deviation (σ) of 12. To calculate the z-statistic, we first compute the standard error (SE):

SE = σ / √n = 12 / √36 = 12 / 6 = 2.

Next, using the z-formula:

z = (M - μ₀) / SE = (70 - 75) / 2 = (-5) / 2 = -2.5.

The calculated z-value of -2.5 exceeds the critical z-value of -1.96 in the negative direction. Since the absolute value of obtained z (|−2.5| = 2.5) is greater than 1.96, this provides evidence to reject the null hypothesis at the 0.05 significance level.

Therefore, we conclude that there is a statistically significant difference in attitudes after watching the film. In words, the data suggest that watching the film on institutionalization has a meaningful impact on students' attitudes toward chronically mentally ill patients, leading to a significant shift from the general population mean score.

In summary, setting alpha at 0.05 means that the researcher is willing to accept a 5% probability of wrongly rejecting the null hypothesis. The hypothesis test conducted was two-tailed, considering any deviation in either direction. The statistical analysis indicated that the observed shift in attitude scores is statistically significant, supporting the conclusion that the film influences students' attitudes towards mental health.

References

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