A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.9 months. Using a 0.05 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times. a. Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)b. What are the degrees of freedom?c. Find a 90% confidence interval for the population standard deviation.