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In: Math

Use the Test Scores Data Set.Preview the document The data consists of standardized test scores over...

Use the Test Scores Data Set.Preview the document The data consists of standardized test scores over several years. Use the techniques you have learned to summarize, present, and describe the data.

Create a confidence interval for the mean score for each year. Use a 95% level of confidence. Clearly explain what the confidence interval means. Does each confidence interval include the population mean for all years? Explain why or why not.
The test scores dropped in 2009. Design and run a hypothesis test to determine if the decline represented a statistically significant decrease in the mean test score. Be sure to explain how you plan set up the test. You will need to decide what you will use as your population. Be sure to explain the result and implications of the hypothesis test.
Is there a significant difference in mean test scores between males and females? Between whites and Hispanics? Design and run hypothesis tests to answer these questions. Explain the set up, results, and implications.
Ask your own question about the data and use confidence intervals or hypothesis tests to answer it.

Write one paper that provides the results from your study. Include an introductory paragraph that describes the data you are working with and makes the reader want to know more. Use at least one paragraph discussing each part of the project. Explain the processes using the technical terms used in the text.

Test Data can be found here: https://docs.google.com/spreadsheets/d/e/2PACX-1vSdSY0cbi4CdW1509-B3HVVGL1t8AieqCPw8nroXMXup8q1Rll3huy8qiCzMphB-DsCOlJ6fNsxlzUO/pubhtml

Solutions

Expert Solution

1)code in R

data = read.csv("../Documents/Tutoring/Software/random data/test_Score.csv")

colnames(data) [1:2] = c("student","test_Score")

#install.packages("dplyr")

library(dplyr)

data %>% group_by(year) %>% summarise(mean_Score = mean(test_Score),sd_Score = sd(test_Score),n_Score = n()) %>%
mutate(se_Score = sd_Score/sqrt(n_Score), lower.ci_Score = mean_Score - qt(1 - (0.05 / 2), n_Score - 1) * se_Score,
         upper.ci_Score = mean_Score + qt(1 - (0.05 / 2), n_Score - 1) * se_Score)

95% confidence interval are in columns lower.ci_Score and upper.ci_Score

we are 95% confident that actual mean lies in this confidence interval

Does each confidence interval include the population mean for all years? Explain why or why not.

No, we are 95% confident only,

Please post next question

+ mutate(se_Score = sd_score/sqrt(n_Score), Tower.ci_Score = mean_Score - qt(- (0.05 / 2), n_Score - 1) * se_score, upper.ci_Score = mean_Score + qt(1 - (0.05 / 2), n_Score - 1) * se_Score) # A tibble: 10 x 7 year mean_Score sd_Score n_Score se_Score lower.ci_Score upper.ci_Score <int> <db7> <db7> <int> <db7> <db7> <db7> 2002 59.6 5.03 210 0.347 58.9 60.3 2003 59.8 5.18 218 0.351 59.1 60.5 2004 60.0 6.67 189 0.485 59.1 61.0 2005 60.4 4.98 217 0.338 59.7 61.0 2006 59.6 4.88 0.337 58.9 60.3 2007 59.9 4.86 190 0.353 59.2 60.6 2008 60.2 5.29 201 0.373 59.4 60.9 2009 58.5 5.59 0.386 57.7 59.2 2010 58.6 5.28 0.362 57.8 59.3 10 2011 60.1 4.88 293 0.285 59.5 60.7 210 210 212


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