8 LARGE-SAMPLE ESTIMATION Problem J: A random sample of n = 300 observations was taken to estimate the binomial proportion 13 of a binomial population. Suppose the sample produced a: = 270 successes. _____ (36) Refer to Problem J. The sample proportion 16 is an unbiased point estimator for the population proportion p. (1) True (2) False _____ (37) Refer to Problem J. Find the (approximate) 95% margin of error. (1) $0.013 (3) $0.034 (2) :|:0.028 (4) :|:0.045 Problem K: The inside diameter a: of a particular type of bearing produced by a manufac- turer is normally distributed. A random sample of size n = 4 bearings was chosen from this population. Suppose the mean of the sample was 0.993 millimeters and the standard deviation 0.0057 millimeters. ,,,,, (38) Refer to Problem K. Find (approximate) a 90% condence interval for a, the average bearing diameter produced by this manufacturer. (1) 0.993 :I: 0.0023 (3) 0.993 :I: 0.0028 (2) 0.993 :I: 0.0047 (4) 0.993 :I: 0.0056 _____ (39) Refer to Problem K. Find (approximate) a 98% condence interval for a, the average bearing diameter produced by this manufacturer. (1) 0.993 :I: 0.0047 (3) 0.993 :I: 0.0066 (2) 0.993 :I: 0.0056 (4) 0.993 :I: 0.0074 _____ (40) Refer to Problem K. Imagine two 99% condence intervals, say 011 and 012. Which of the statements below is true if CI1 is based on a sample size of n = 4, and (Hg on a sample size of n = 100? (1) Interval (3'12 is ve times as wide as interval 011. (2) Interval CI2 is twentyve times as wide as interval CI 1. (3) Interval 011 is ve times as wide as interval CI2. (4) Interval (3'11 is twentyve times as wide as interval (3'12