A sociologist is testing the null hypothesis that the percentage of school superintendents who earn an annual salary of more than $150,000 is greater than or equal to 50%. The sociologist conducts a poll of 1100 randomly selected superintendents and finds that 565 earn more than $150,000. Based on this poll, the sociologist should make what conclusion at a 5% level of significance?

Please help. I don't really know which formula to use, but if you could even give me that, I would really appreciate it.

Ms. Kim Mooney in 1989 as part of completing her dissertation at UNH. The dataset was collected to assist in exploring the relationship between the “effect of social stress on blood pressure.” This was investigated by collecting data at six different points (i. preliminary baseline, ii. second baseline, iii. rehearsal and preparation for role play, iv. stressful role play exercise, v. first baseline follow-up, vi. second baseline follow-up). You will need to install the PASW Grad Pack 18.0 in order to download the dataset.

Ms. Mooney collected data on the Rathus Assertiveness scale and the Crowne Marlowe Social Desirability Scale, which contained subscales for “anger in” (the tendency to hold anger “in”), and “anger out” (the tendency to “express anger openly”).

Employing this data, we would like to explore the relationship between assertiveness and the tendency to express anger openly. We will examine a Pearson’s r to help us examine this relationship. Then, we will examine the relationship between assertiveness and whether one holds anger “in.” To explore this question, we will run a bivariate regression procedure.

Open the SPSS dataset complete_mooney_bp.sav into SPSS.

Choose "analyze," then "correlate," then "bivariate." Move the variables "rath" and "axout" into the “Variables” window (these are respectively the measures of assertiveness and the tendency to “express anger openly.”)

Make sure “Pearson” is checked in the Correlation Coefficient window. Choose "options," check "means and standard deviations" in the Statistics window, then check "continue," then "OK" to run the analysis.

Based on this analysis, answer the following questions:

What are the means and standard deviations of the two variables, “rath” and “axout”?
What is the Pearson r?
What is the p value (“significance level”)? What does this p value mean?
How does the n (sample size) of this sample affect the r and p values?
Now, we turn our attention to our bivariate regression question. Is there a relationship between assertiveness and whether one holds anger “in”?

please help. feel like i'm lost in space.

To determine the conclusion, we need to conduct a hypothesis test. In this case, we are testing the null hypothesis (H0) that the percentage of school superintendents who earn an annual salary of more than $150,000 is greater than or equal to 50%. The alternative hypothesis (H1) would be that the percentage is less than 50%.

To perform this hypothesis test, we can use a one-sample proportion test.

Here's how to calculate it step by step:

1. State the null hypothesis (H0) and alternative hypothesis (H1):
- Null hypothesis (H0): The percentage of school superintendents earning more than $150,000 (p) is equal to or greater than 50%.
- Alternative hypothesis (H1): The percentage of school superintendents earning more than $150,000 (p) is less than 50%.

2. Determine the level of significance (α) - in this case, it is given as 5% (0.05).

3. Collect the data: The sociologist conducted a poll of 1100 randomly selected superintendents and found that 565 earn more than $150,000.

4. Compute the test statistic:
- Calculate the observed proportion (p̂): p̂ = (number of successes) / (sample size)
In this case, p̂ = 565/1100 = 0.5136

- Calculate the standard error (SE):
SE = √[(p̂ * (1 - p̂)) / n]
SE = √[(0.5136 * (1 - 0.5136)) / 1100] = 0.015

- Calculate the test statistic (Z-score):
Z = (p̂ - p0) / SE
p0 represents the hypothesis value from H0, which is 0.50 in this case.
Z = (0.5136 - 0.50) / 0.015 = 0.9067

5. Determine the p-value:
The p-value is the probability of observing a test statistic as extreme as the observed value (or more extreme) under the assumption that the null hypothesis is true.
To determine the p-value, we can use a Z-table or a statistical software. The p-value for Z = 0.9067 is approximately 0.181 (or 18.1%).

6. Make a decision:
Compare the p-value to the level of significance (α):
- If the p-value is less than α (0.05), we reject the null hypothesis (H0) in favor of the alternative hypothesis (H1). In this case, we conclude that there is evidence to suggest that the proportion of school superintendents earning more than $150,000 is less than 50%.
- If the p-value is greater than or equal to α (0.05), we fail to reject the null hypothesis (H0). In this case, we conclude that there is not enough evidence to suggest that the proportion is less than 50%.

In this scenario, the calculated p-value (18.1%) is greater than the significance level (5%). Thus, we fail to reject the null hypothesis. The sociologist should conclude that there is not enough evidence to suggest that the percentage of school superintendents who earn an annual salary of more than $150,000 is less than 50%.

Null hypothesis:

Ho: p > or = .50 -->meaning: population proportion is greater than or equal to .50
Alternative hypothesis:
Ha: p < .50 -->meaning: population proportion is less than .50

Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = .51 - .50 -->test value (565/1100 = .51) minus population value (.50)
divided by
√[(.50)(.50)/1100]

Therefore, after doing the above calculation, you should find that the test statistic will not exceed the critical value at the 5% level of significance. You cannot reject the null if this is the case.