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Chronicle data shows the average salary of instructors in Washington state is $63241 with a population standard deviation of $3500. A claim was made that instructors at a certain university in the state earns lower than this amount. A random sample of 30 instructors from this university was selected, and it was revealed that the average salary is $55,700. a. Construct a 95% confidence interval for the average salary of instructors based on the data gathered from the sample. b. Test at 5% level of significance if the data provide evidence to support the claim. Assume the sample standard deviation is $4000. c. If the researchers want to estimate the average salary at a 99% confidence level with only $1000 error on the estimate, how many samples are needed