PLEASE USE THE PROGRAMMING LANGUAGE R TO SOLVE THE FOLLOWING QUESTION:

PLEASE USE THE PROGRAMMING LANGUAGE R TO SOLVE THE FOLLOWING QUESTION:

Current methods for identification of malignant kidney tumors that require surgical removal are imprecise and result in misidentification of non-malignant fatty tumors as malignant 25% of the time. A new method for this identification based on NMRI spectroscopy is being tested in a clinical trial to determine if its misidentification rate is lower than current methods. Suppose a random sample of 250 patients with non-malignant kidney tumors is tested with the NMRI method and 51 patients had tumors that were misidentified as malignant.

a) Is the misidentification rate for the new method lower than 25% at the 5% level of significance?

b) Construct a 90% confidence interval for the misidentification rate of the new method.

c) What is the probability the null hypothesis would be rejected with a sample of size 250 if the misidentification rate in the population is 20%? Suppose a clinical trial can be run using a random sample of 500 patients. What would be the probability this trial would reject the null hypothesis if the misidentification rate is 20%?

d) What sample size would be required to estimate this rate to within 0.02 of the actual value with 95% confidence if it is assumed the rate is no more than 0.25?

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