Conducting A Z-Test Researcher Predicts Watching A Film

Conducting a z-Testa Researcher Predicts That Watching A Film On Insti

Conducting a z-Testa researcher predicts that watching a film on institutionalization will change students’ attitudes about chronically mentally ill patients. The researcher randomly selects a class of 36 students, shows them the film, and gives them a questionnaire about their attitudes. The mean score on the questionnaire for these 36 students is 70. The score for people in general on this questionnaire is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level (i.e., alpha = .05), does showing the film change students’ attitudes towards the chronically mentally ill? What does it mean to set alpha at .05? What is your null hypothesis? Alternate hypothesis? Is this a one-tailed or two-tailed hypothesis? What is the critical z? Calculate the obtained z. Do you reject or fail to reject the null hypothesis? State in words what you have found.

Paper For Above instruction

Introduction

Hypothesis testing is a fundamental aspect of inferential statistics that allows researchers to determine whether observed data are consistent with a specified hypothesis, typically the null hypothesis. In this scenario, a researcher aims to ascertain whether viewing a film about institutionalization influences students’ attitudes toward chronically mentally ill patients. By employing a z-test, the researcher compares the mean attitudes of the students who watched the film to the general population’s mean. This analysis involves clear formulation of hypotheses, selecting an appropriate significance level, calculating the z statistic, and interpreting the results within the context of the study.

Step 1: Setting the Hypotheses

The null hypothesis (H₀) posits that the film has no effect on students’ attitudes; therefore, the mean attitude score of the students remains the same as the general population mean. Mathematically:

H₀: μ = 75

The alternative hypothesis (H₁) suggests that watching the film does alter students’ attitudes, which could be either an increase or a decrease. Since the researcher is interested in any change, regardless of direction, this is a two-tailed hypothesis:

H₁: μ ≠ 75

Choosing a two-tailed test allows for detection of deviations in either direction, positive or negative, from the population mean.

Step 2: Significance Level and Critical z

The significance level, alpha (α), is set at 0.05, meaning the researcher is willing to accept a 5% probability of rejecting the null hypothesis when it is actually true (Type I error). For a two-tailed test with α = 0.05, the critical z-values are split equally across both tails, each with an area of 0.025. The critical z-values are approximately ±1.96. That is, if the calculated z-score surpasses ±1.96 in magnitude, the null hypothesis will be rejected.

Step 3: Calculating the Test Statistic (z)

The z statistic measures how many standard errors the sample mean is away from the population mean. The formula is:

z = (M - μ) / (σ / √n)

Where:

- M = 70 (sample mean)

- μ = 75 (population mean)

- σ = 12 (population standard deviation)

- n = 36 (sample size)

Calculate the standard error (SE):

SE = σ / √n = 12 / √36 = 12 / 6 = 2

Now, compute z:

z = (70 - 75) / 2 = (-5) / 2 = -2.5

The calculated z-score is -2.5.

Step 4: Decision Rule

Comparing the calculated z-value to the critical z-values:

- Since |−2.5| = 2.5 > 1.96, the z-score falls into the rejection region.

Therefore, we reject the null hypothesis at the 0.05 significance level.

Step 5: Conclusion and Interpretation

Rejecting the null hypothesis indicates that there is statistically significant evidence to suggest that watching the film has an effect on students’ attitudes toward the chronically mentally ill. The negative z-value suggests that the students’ attitudes, as measured by the questionnaire, have become more negative or less favorable compared to the general population after watching the film. This outcome implies that the film may have influenced students’ perceptions, warranting further investigation into the content and its impact.

Additional Insights

It is important to consider that statistical significance does not imply practical significance. The magnitude of the change (an average score decrease of 5 points) should be examined in context to determine whether it reflects a meaningful shift in attitudes. Furthermore, future research might explore qualitative aspects or longitudinal effects to assess whether these attitude changes persist over time.

Conclusion

In summary, the hypothesis testing procedure revealed that viewing the film on institutionalization statistically significantly affected students’ attitudes, based on the collected data and the set significance level of 0.05. The null hypothesis asserting no change was rejected, indicating that the film likely influenced the students’ perceptions about the mentally ill, albeit with further exploration needed to understand the nature and implications of this influence.

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