NIST (National Institute of Standards and Technology) would like to test the average heat capacity of a new type of composite material. To that end, the scientists at the NIST test the heat capacity of 10 different samples of this new material. Here are the results of these experiments:

Sample #Heat capacity of the sample (Joule / Kelvin)

12.05

21.98

32.01

41.84

52.13

62.00

71.78

81.89

91.96

101.91

Given the data reported above, the scientists would like to test the hypothesis that the average heat capacity of this new composite material is equal to 2 joules / kelvin. Using a 98% confidence level, test this hypothesis.

Do not forget to explicitly write the null hypothesis, alternative hypothesis, the critical value used for testing and the test statistic itself.