Answer this question in R. Show as much of your work as possible. This question utilizes the BookPrices data set found in the resampledata package.This data set contains the book prices of all textbooks from mathematics and thenatural and soocial sciences at a specific university. Determine if there is evidence ofa significant difference between the average prices of Math & Science books versusSocial Science books at this particular university.

The data to be used in R is BookPricesThe sample data obtained from R is as followsIt is required to determine if there is a significant difference in the average prices between Math & Science books and Social Science books.Let μMS be the mean of Math & Science and μSS be the mean of Social Sciences . Then, in order to determine if there is a significant difference between the 2 samples, the appropriate hypotheses to be tested are,Null Hypothesis: There is no significant difference in the average prices between Math & Science and Social Science books.H0:μMS=μSSAlternative Hypothesis: There is a significant difference in the average prices between Math & Science books and Social Science books.H1:μMS≠μSSThe above-defined hypothesis can be tested using the two-sample t-test under the assumption of equality of variances The test statistic is given byRejection rule:Let α be some defined level of significance (generally, if α value is not defined, as a rule of thumb α=0.05 is considered for testing the hypothesis.If the p-value from the above test statistic is less than α then reject the null hypothesis otherwise the test fails to reject the null hypothesis.The steps involved in testing the H0 vs H1 are as follows.Install the package resampledata and load the package in R Load the data BookPricesSeparate the data into two groups: Math & Science and Social SciencePerform a t-test for independent samples using the R inbuilt function t.test()Extract the p-value from the result and make the decisions at the defined α value.The R-code for the above-explained steps is as follows1# Install the packege 2 install.packages('resampledata') 3 4# Load the resampledata package into R 5 library(resampledata) 6 7# Load the BookPrices dataset 8 data(BookPrices) 9 10 11# Separate the data into two groups: Math & Science and Social Science 12 math_science_prices <- BookPrices$Price[BookPrices$Area == 'Math & Science'] 13 social_science_prices <- BookPrices$Price[BookPrices$Area == 'Social Sciences'] 14 15# Perform a t-test for independent samples under the assumption of equality of variances 16 t_test_result <- t.test(math_science_prices, social_science_prices,var.equal = TRUE) 17 18# View the results 19 print(t_test_result) 20 21#Define the level of significance 22 alpha <- 0.05 23 24#Extract the p-value from the t-test results (rounded to 4 decimal places) 25 p_value <- round(t_test_result$p.value,4) 26 27 28# Interpret the results 29 if (p_value < 0.05) { 30 cat("Since p-value =",p_value, "is < alpha =", alpha, ", there is evidence of a significant difference in average prices.\n") 31 } else { 32 cat("Since p-value =",p_value, "is >= alpha =", alpha, ", there is no significant difference in average prices.\n") 33 } 34 35The R-output is as followst-test results:The final Conclusion :From the t-test results obtained from RThe t-test statistic is, t=3.4522The p-value is 0.0013The defined level of significance, α=0.05Conclusion: Since the p−value<0.05, reject the null hypothesis and conclude that there is a significant difference in the average prices between Math & Science and Social Science books.