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Created: Apr 27, 2015
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The proportion of certified teachers that believe their salary should be merit-based.
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This report was completed through the use of a StatCrunch survey about the proportion of certified teachers who believe their salary should be merit-based (i.e. determined through their students' success).  The survey can be found at: http://www.statcrunch.com/5.0/survey.php?surveyid=10778&code=IEFKO.

 

Data set 1. Rachael Martin2   [Info]
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Question 1: Are you a certified teacher who is currently employed in a public school? (Y/N) Upon closing the survey to public, 41 valid responses were collected, meaning 41, certified and employed teachers submitted their opinion on merit-based teacher salary.

Question 2: Which topic of study do you teach? (Liberal arts, math, science, English, social studies, other) The frequency table below shows that of the teachers who participated in this survey, 3 teach English/Language Arts, 7 teach Liberal arts, 9 teach Mathematics, 6 teach Science, 5 teach Social Studies/History, and 11 teach a subject other than what specified.

Result 1: Frequency Table_Subject Taught   [Info]
Frequency table results for Subject Taught:
Count = 41
Subject TaughtFrequencyRelative Frequency
English/Language Arts30.073170732
Liberal arts70.17073171
Mathematics90.2195122
Other110.26829268
Science60.14634146
Social Studies/History50.12195122

Question 3: How long have you held your current position? (enter a numerical answer in years, please include current academic year in total) The table below illustrates the range of experience, in academic years, of the teachers who participated in the survey. Results indicate that the majority of teachers in this survey are newer to their position (1-5 years). The most experienced teacher involved has been employed in their position for 20 academic years.

Result 2: Frequency Table_Yrs in Pos   [Info]
Frequency table results for Years in Position:
Count = 41
Years in PositionFrequencyRelative Frequency
170.17073171
280.19512195
350.12195122
440.097560976
540.097560976
620.048780488
730.073170732
810.024390244
910.024390244
1010.024390244
1110.024390244
1310.024390244
1420.048780488
2010.024390244

Question 4: Do you believe a teacher’s salary should be based on merit (i.e. the measured success of their students)? (Y/N/No opinion) The responses to this question are found below and indicate that 20 teachers out of the 41 surveyed, or 61% believe that their salary should not be merit-based. 13/41 or 32% respondents believe that their salary should be based on merit, or the success of their students. The remaining 3/41 teachers, or 7%, have no opinion on the merit-pay debate.

Result 3: Frequency Table_Y/N Merit Salary   [Info]
Frequency table results for Merit-based Salary:
Count = 41
Merit-based SalaryFrequencyRelative Frequency
No250.6097561
No opinion30.073170732
Yes130.31707317

Question 5: Do you believe that merit-based pay is an appropriate way to compensate a teacher on their performance? (Y/N/No opinion) The table below indicates that 24/41, or 59%, of the teachers surveyed believe merit-based pay is not an appropriate way to compensate teachers. However, 16/41 or 39%, feel that merit pay is an appropriate determinant for teacher salary, and 1/41 or 2% had no opinion on the appropriateness of merit-pay for teachers.

Result 4: Frequency Table_Merit Pay Approp   [Info]
Frequency table results for Merit-Pay Appropriateness:
Count = 41
Merit-Pay AppropriatenessFrequencyRelative Frequency
No240.58536585
No opinion10.024390244
Yes160.3902439

This bar plot shows us that the greatest number of teachers surveyed answered "no" to having their salary be based on their students' academic success. About half the number of teachers who answered "no" responded "yes" to having their salary based on the success of their students. The least occurring response was "no opinion". This bar plot illustrates the results to question 5 of the survey.

Result 5: Bar Plot for Parameter Q   [Info]
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This pie chart shows us that 64.5% of the teachers surveyed do not feel that merit pay is appropriate, 33.01% feel that it is appropriate, and 2.43% have no opinion on the appropriateness of merit pay.

Result 6: Pie Chart With Summary   [Info]
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This combined bar plot shows us the demographic of the teachers surveyed in displaying the years that they have held their current position compared to the subject taught. We see that the greatest percentage of teachers who participated in this survey teach a subject "other" than the options which were provided, followed by math, liberal arts, science, history, and English respectively. Of those results, the greatest percentage of teachers that were surveyed have 1-5 years of experience in their current position.

Result 7: Years in position for Subject taught   [Info]
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This scatter plot shows us the effect that experience has in relation to a teacher's stance on merit-based salaries. We can observe that with greater years of experience, a teacher is likely to answer "no" to having a merit-based salary.

Result 8: Effect of Experience on Merit Pay Opinion   [Info]
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1.The sample is a convenience sample.  It is like to be biased because it is a self-selected sample and consists of certified teachers with strong feelings about the issue of merit-based pay.  This sampling method used the results that were readily available, a predominant characteristic of convenience sampling.  Additionally, because participation was voluntary, participation bias is inevitable. 

2. Question 1: Are you a certified teacher who is currently employed in a public school? (Y/N)

Question 2: Which topic of study do you teach? (Liberal arts, math, science, English, social studies, other)

Question 4: Do you believe a teacher’s salary should be based on merit (i.e. the measured success of their students)? (Y/N/No opinion)

Question 5: Do you believe that merit-based pay is an appropriate way to compensate a teacher on their performance? (Y/N/No opinion) 

·      Qualitative data and nominal measurement types were used for these questions because the responses consist of nonnumeric answers that cannot be ranked or ordered.

Question 3: How long have you held your current position? (Enter a numerical answer in years, please include current academic year in total)

·      This question collected quantitative data because it consisted of values that represented counts/measurements.  The data was also discrete because only distinct values (whole integers representing years) could be recorded.  The level of measurement was at the ratio level because intervals (differences) and ratios are meaningful and a true zero exists (zero years=no experience).

3. According to the data collected through this survey, the proportion of certified teachers that actually believed that their salary should be merit-based, and answered “Yes” to question number four, was 13/41 or 32% or 0.32. The standard deviation of our population proportion or sampling distribution therefore can be determined using:

s=

https://waubonsee.blackboard.com/bbcswebdav/pid-446275-dt-content-rid-2059583_1/xid-2059583_1

When p= 0.40 and n=41. s=√0.4(1-0.4)/41=√0.0059=0.07≈0.10. If we want to analyze how our survey sample results compare to expected results, we can find the z-score, which will determine how many standard deviations our sample proportion is from the peak of the sampling distribution (=mean or population proportion). The formula to do this is: z = (sample proportion - population proportion)/sample s.d.= (0.32-0.40)/0.10= -0.8.  In other words, the sample used in the poll has a proportion that is 0.8 standard deviations below the peak of the distribution of the sample proportions.

4. a. The claim of this survey states: The proportion of certified teachers employed in a public school that believe their salary should be merit-based is less than 40%.

b.  The null hypothesis is the claim that the proportion of certified teachers that believe their salary should be merit-based is 40% or 0.40. Ho (null hypothesis): p= 0.40.

The alternative hypothesis is the claim that the proportion of certified teachers that believe their salary should be merit based is less than 40% or 0.40. Ha (alternative hypothesis): p<0.40.

c. The alternative hypothesis for this survey requires a left-tailed hypothesis test, because it requires testing whether the population parameter lies to the left (lower values) of the claimed values.  

d. The sample statistic of this survey includes: The proportion of certified teachers in our sample that believe their salary should be merit-based is p-hat= 32% or 0.32, given the sample size of n=41.

e. This survey will use t-distribution, which was determined using the flow chart below and through application of the definition of “t-distribution”. Because the standard deviation of the entire population is unknown and our sample size is greater than 30 (n=41), we can infer that t-distribution is most appropriate for this survey.

https://waubonsee.blackboard.com/bbcswebdav/pid-446283-dt-content-rid-2059601_1/xid-2059601_1

f. The test statistic is calculated using the formula: z = (sample proportion - population proportion)/sample s.d. Using the calculations from question #3 [(0.32-0.40)/0.10= -0.8], we determined the standard score for our survey to be -0.80, which has a corresponding P-value of 0.2119.

g. We decide whether to reject or to fail to reject the null hypothesis by comparing the standard score (z) for our sample distribution to the critical value at the 0.05 significance level.  Since this survey is a left-tailed hypothesis test, we reject the null hypothesis if the standard score is less than or equal to the critical value (z≤-1.645). Our standard score of -0.80 is greater than the critical value of -1.645, so our results are not significant at the 0.05 level.  The P-value of 0.2119 that corresponds to our z-score confirms that there is a greater than 0.05 probability that this sample would arise if the null hypothesis is true. 

h. In conclusion, because the test does not meet the criterion for significance at the 0.05 level, we fail to reject the null hypothesis.  Moreover, this survey did not provide sufficient evidence to support the claim that the proportion of certified teachers employed in a public school that believe their salary should be merit-based is less than 40%.

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