QUESTION
A school counselor wants to compare the effectiveness of an online SAT preparation program with an in-person SAT preparation class. For an experiment, the counselor recruits 30 students who have already taken the SAT once. The response variable will be the improvement in SAT score. Which design do you prefer? Explain your answer.
QUESTION
A school counselor wants to compare the effectiveness of an online SAT preparation program with an in-person SAT preparation class. For an experiment, the counselor recruits 30 students who have already taken the SAT once. The response variable will be the improvement in SAT score. Design an experiment that uses a completely randomized design to investigate this question.
QUESTION
A school counselor wants to compare the effectiveness of an online SAT preparation program with an in-person SAT preparation class. For an experiment, the counselor recruits 30 students who have already taken the SAT once. The response variable will be the improvement in SAT score. Design an experiment that uses a matched pairs design to investigate this question. Explain your method of pairing.
ALGEBRA2
A school offered an optional, free SAT prep class for juniors. Students could choose whether to attend the class. Juniors who took the class, on average, scored 300 points higher on the SAT than their classmates who did not attend the class. The principal says this proves the class is very successful and should be offered again next year. a. State at least one reason the principal might be wrong about the class. b. State one way enrollment in the SAT prep class could have been changed to provide a better measurement of the relationship between taking the SAT prep class and a student's score on the SAT.
ALGEBRA2
Consider the question: "Does a traditional classroom SAT preparation course improve scores more than an online study course? " Design an experiment that could help to answer this question.
STATISTICS
Suppose an SAT preparation course makes the following statement in their advertising brochure: "We asked our graduates to report on their SAT scores before and after taking our course. The mean increase in SAT scores for the 500 graduates who responded was 210 points." Describe how nonresponse might lead to bias in this study. Is the mean of 210 points likely greater than or less than the actual mean increase for all graduates of the course?
STATISTICS
Use the data in the table below. The values are based on a scatterplot in "An SAT Coaching Program That Works," by Jack Kaplan, Chance, Vol. 15, No. 1. The values are math SAT scores of students before and after taking an SAT preparation course. $$ \begin{matrix} \text{Before} & \text{460} & \text{470} & \text{490} & \text{490} & \text{510} & \text{510} & \text{600} & \text{620} & \text{610}\\ \text{After} & \text{480} & \text{510} & \text{500} & \text{610} & \text{590} & \text{630} & \text{630} & \text{660} & \text{690}\\ \end{matrix} $$ Find the mean, median, range, standard deviation, and variance of the before scores.
STATISTICS
Use the data in the table below. The values are based on a scatterplot in "An SAT Coaching Program That Works," by Jack Kaplan, Chance, Vol. 15, No. 1. The values are math SAT scores of students before and after taking an SAT preparation course. $$ \begin{matrix} \text{Before} & \text{460} & \text{470} & \text{490} & \text{490} & \text{510} & \text{510} & \text{600} & \text{620} & \text{610}\\ \text{After} & \text{480} & \text{510} & \text{500} & \text{610} & \text{590} & \text{630} & \text{630} & \text{660} & \text{690}\\ \end{matrix} $$ Construct a scatterplot. Does there appear to be a correlation between the before scores and the after scores?
STATISTICS
A national chain of SAT-preparation schools wants to know if using a smartphone app in addition to its regular program will help increase student scores more than using just the regular program. On average, the students in the regular program increase their scores by 128 points during the 3-month class. To investigate using the smartphone app, a random sample of 5000 students uses the app along with the regular program. After 3 months, the average improvement was $\bar{x}=130$ with a standard deviation of $s_{x}=65.$ Is there convincing evidence at the $\alpha=0.05$ significance level that the average score increase for students who use the smartphone app in addition to the regular program is greater than 128 points?
STATISTICS
Use the data in the table below. The values are based on a scatterplot in "An SAT Coaching Program That Works," by Jack Kaplan, Chance, Vol. 15, No. 1. The values are math SAT scores of students before and after taking an SAT preparation course. $$ \begin{matrix} \text{Before} & \text{460} & \text{470} & \text{490} & \text{490} & \text{510} & \text{510} & \text{600} & \text{620} & \text{610}\\ \text{After} & \text{480} & \text{510} & \text{500} & \text{610} & \text{590} & \text{630} & \text{630} & \text{660} & \text{690}\\ \end{matrix} $$ Test for a linear correlation between the before scores and the after scores. If there is a linear correlation, does that mean that the preparation course is effective? Why or why not?
QUESTION
A national chain of SAT-preparation schools wants to know if using a smartphone app in addition to its regular program will help increase student scores more than using just the regular program. On average, the students in the regular program increase their scores by 128 points during the 3-month class. To investigate using the smartphone app, the prep schools have 5000 students use the app along with the regular program and measure their improvement. Then the schools will test the following hypotheses: $H_{0}: \mu=128$ versus $H_{a}: \mu>128,$ where $\mu$ is the true mean improvement in the SAT score for students who attend these prep schools. After 3 months, the average improvement was $\bar{x}=130$ with a standard deviation of $s_{x}=65.$ The standardized test statistic is l = 2.18 with a P-value of 0.0148. Explain why this result is statistically significant, but not practically important.
PROBABILITY
One year 37 students sat an examination in Physics, 48 sat Chemistry and 45 sat Biology. 15 students sat Physics and Chemistry, 13 sat Chemistry and Biology, 7 sat Physics and Biology and 5 students sat all three. a) Draw a Venn diagram to represent this information. b) Calculate $n(P \cup C \cup B)$
STATISTICS
Is $1900$ SAT score a good score on a SAT test if the mean score is $1240$ and the standard deviation is $270$ and SAT scores are distributed normally ?
ENGINEERING
When a saturated vapor condenses on a vertical, isothermal flat plate in a continuous film, the rate of heat transfer is proportional to(a) $(T_s – T_{sat})1/4$ (b) $(T_s – T_{sat})1/2$ (c) $(T_s – T_{sat})3/4$ (d) $(T_s – T_{sat})$ (e) $(T_s – T_{sat})2/3$
QUESTION
The regression line relating verbal SAT scores and college GPA is Average GPA = 0.539 + 0.00362 (Verbal SAT) Estimate the average GPA for those with verbal SAT scores of 600. Explain what the slope of 0.00362 represents in terms of the relationship between GPA and SAT. For two students whose verbal SAT scores differ by 100 points, what is the estimated difference in college GPAs? Explain whether the intercept has any useful interpretation in the relationship between GPA and verbal SAT score. Keep in mind that the lowest possible verbal SAT score is 200.
CALCULUS
The average SAT mathematics scores of incoming students at an eastern liberal arts college have been declining in recent years. In 2006, the average SAT score was 575; in 2011, it was 545. Assuming the average SAT score varies linearly with time, answer these questions. (a.) Express the average SAT score in terms of time measured from 2006. (b.) If the trend continues, what will the average SAT score of incoming students be in 2024$? (c.) When will the average SAT score be 455?
QUESTION
A study finds that high school students who take the SAT, enroll in an SAT coaching course, and then take the SAT a second time raise their SAT mathematics scores from a mean of 521 to a mean of 561. What factors other than taking the course might explain this improvement?
CHEMISTRY
Let $P_{1}^{\text {sat }} \text { and } P_{2}^{\text {sat }}$ be values of the saturation vapor pressure of a pure liquid at absolute temperatures $T_{1} \text { and } T_{2}.$ Justify the following interpolation formula for estimation of the vapor pressure $P^{\mathrm{sat}}$ at intermediate temperature T: $\ln P^{\text {sat }}=\ln P_{1}^{\text {sat }}+\frac{T_{2}\left(T-T_{1}\right)}{T\left(T_{2}-T_{1}\right)} \ln \frac{P_{2}^{\text {sat }}}{P_{1}^{\text {sat }}}$
STATISTICS
Is $1020$ a good SAT score if the mean score is $1060$ and the standard deviation is $217$ and SAT scores are distributed normally ?
STATISTICS
A study is made of Math and Verbal SAT scores for the entering class at a certain college. The summary statistics: $$ \text { average } M - S A T = 560 , \quad S D = 120 $$ $$ \text { average V-SAT } = 540 , \quad \mathrm { SD } = 110 , \quad r = 0.66 $$ The investigator uses the SD line to predict V-SAT score from M-SAT score. a) If a student scores 680 on the M-SAT, the predicted V-SAT score is ______. b) If a student scores 560 on the M-SAT, the predicted V-SAT score is _____. c) The investigator's r.m.s. error is _____ $$ \sqrt { 1 - 0.66 ^ { 2 } } \times 110 $$ . Options: $$ \text greater than \quad equal to \quad less than $$ If more information is needed, say what you need, and why.
CALCULUS
The average scores of incoming students at an eastern liberal arts college in the SAT mathematics examination have been declining at a constant rate in recent years. In 2005, the average SAT score was 575, while in 2010 it was 545. a. Express the average SAT score as a function of time. b. If the trend continues, what will the average SAT score of incoming students be in 2015? c. If the trend continues, when will the average SAT score be 527?
STATISTICS
SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114. (a) What percentage of SAT scores is between 401 and 629? (b) What percentage of SAT scores is less than 401 or greater than 629? (c) What percentage of SAT scores is greater than 743?
STATISTICS
About 1.5 million high-school students took the SATs in 2005. The regression equation for predicting the Math SAT score from the Verbal SAT score is $$ \text { predicted M-SAT } = 0.6 \times \mathrm { V-SAT } + 220 $$ The r.m.s. error of the regression line is 80 points. (The scatter diagram is football-shaped; numbers have been simplified a little.) About 50,000 students scored 500 points on the V-SAT. Of these students, about how many scored better than 500 on the M-SAT? Or do you need more information?
STATISTICS
Is $1700$ a good score on SAT test if the mean score is $1150$ and the standard deviation is $250$ and SAT scores are distributed normally ?
PSYCHOLOGY
Why was the SAT recently renamed?