The exercise will involve analysing the given data for the tuition fees for a three-year management degree program in India by answering the questions that follow. Below is the data set for twenty universities of India based on their type, government or private.

Type of College

FeesPrivate

778500

Private375000Private264000Private312000Private597000Private312000Government80000Government25000Private413000Private258000Private73200Private495000Government69000Government60744Government16280Government41000Private312500Private476200Private275000Private523000

Calculate the mean and standard deviation for the given data.

According to a report by a reputed Indian educational web portal, the average fee of an undergraduate degree in management in India is greater than or equal to Rs. 4,10,000. Check if this claim is statistically valid at 5% level of significance.