Do cash incentives improve learning? A high-school teacher in a low-income urban school in Worcester, Massachusetts,...

Do cash incentives improve learning? A high-school teacher in a low-income urban school in Worcester, Massachusetts, used cash incentives to encourage student learning in his AP Statistics class. In 2010, 15 of the 80 students enrolled in his class scored a 5 on the AP Statistics exam. Worldwide, the proportion of students who scored a 5 in 2010 was 0.15. Is this evidence that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15?

Conduct a hypothesis test at the significance level α = 0.05 to determine if evidence is present regarding the use of cash incentives to motivate AP Statistics students to do better on their AP exams.

Solutions

Expert Solution

we want to test that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15.

Ho:- P = 0.15 vs Ha:- P > 0.15

ie. Ho:- The proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is not higher than the worldwide proportion of 0.15.

Ha:- The proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15.

In 2010, 15 of the 80 students enrolled in his class scored a 5 on the AP Statistics exam.

n = total number of students enrolled = 80

x= number of students scored 5 = 15

p= proportion of students scored 5 out of 80 = x/n = 15/80 = 0.1875

the significance level α = 0.05

P-value = P( Z > Zcal )

= P( Z > 0.939 )

= 0.1378 ........from normal distribution

Reject Ho if P-value < alpha

P-value = 0.1378 > α = 0.05

We fail to reject Ho at 5% l.O.S

We may conclude that there is No sufficient evidence that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A high school teacher is interested to compare the average time for students to complete a...

A high school teacher is interested to compare the average time for students to complete a standardized test for three different classes of students. The teacher collects random data for time to complete the standardized test (in minutes) for students in three different classes and the dataset is provided below. The teacher is interested to know if the average time to complete the standardized test is statistically the same for three classes of students. Use a significance level...

To improve exports, should the dollar be valued high or low? Explain.

Previous Question: The mean store for an exit text at an urban high school examination was...

Previous Question: The mean store for an exit text at an urban high school examination was 68% with a standard deviation of 3. Given these results, what percentage of students fall under the mean? 25% 50% 60% 75% Using the same data from the question above, what scores will fall within one standard deviation above and one standard deviation below the mean? 66 to 72 60 to 74 65 to 71 58 to 81

Distinguish between a low and high income and a low and high economic growth rate. What...

Distinguish between a low and high income and a low and high economic growth rate. What are the key features of an economy that are present when incomes are high or fast growing and absent when incomes are low and stagnating or growing slowly? Provide an example of an economy with a low income and slow growth rate, a low income and rapid growth rate, and a high income with sustained growth over many decades.

A teacher was interested in the mathematical ability of graduating high school seniors in her state....

A teacher was interested in the mathematical ability of graduating high school seniors in her state. She gave a 32-item test to a random sample of 15 seniors with the following results: mean = 1270, and standard deviation = 160. Find the 95% confidence interval and write a sentence describing what it means. Show your work.

Dolores used to work as a high school teacher for $40,000 per year but quit in...

Dolores used to work as a high school teacher for $40,000 per year but quit in order to start her own catering business. To invest in her factory, she withdrew $20,000 fromher savings, which paid 5 percent interest, and borrowed $30,000 from her uncle, whom she pays 4 percent interest per year. Last year she paid $25,000 for ingredients and had revenue of $60,000. She asked Louis the accountant and Greg the economist to calculate her profit for her. Explicit...

This question is an extension from Q2 above. The high school teacher was also interested in...

This question is an extension from Q2 above. The high school teacher was also interested in whether there is a gender difference in terms of the student’s choice of majors. So he broke the data down by gender in the following table and conducted a Chi-square test for independence with α = .05. Type of Major Female Male Total STEM 10 25 35 Social Sciences 11 9 20 Liberal Arts 7 3 10 a. What are the variables in this...

A high school physics teacher wondered if his students in the senior class this year will...

A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM (Science, Technology, Engineering, Mathematics) majors than Social Science and Liberal Arts majors. He asked each of his 65 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly. 35...

Table 22-13 A high school Spanish class and their teacher are planning to take a Spring...

Table 22-13 A high school Spanish class and their teacher are planning to take a Spring Break trip abroad but they have to decide where to go. They have narrowed the options to: Spain, Mexico, Ecuador, and Costa Rica. The voters’ preferences are shown in the table below. Voter First Choice Second Choice Third Choice Fourth Choice 1 Spain Mexico Ecuador Costa Rica 2 Costa Rica Mexico Ecuador Spain 3 Spain Mexico Ecuador Costa Rica 4 Ecuador Costa Rica Mexico...

A high school teacher hypothesizes a negative relationship between performance in exams and performance in presentations....

A high school teacher hypothesizes a negative relationship between performance in exams and performance in presentations. To examine this, the teacher computes a correlation of -0.23 from a random sample of 29 students from class. What can the teacher conclude with α = 0.01? a) Obtain/compute the appropriate values to make a decision about H0. (Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.) critical value = ; test statistic = Decision: ---Select one--- (Reject...

Subjects