A sample of 10 measurements of the radius of a marble gave a mean of 4.38mm and a standard deviation of 0.06mm. Find a 99% confidence interval for the actual radius. b) In measuring ignition duration, an engineer estimates that the standard deviation is 0.05 seconds. How large a sample of measurements must he take in order to be 95% confident that the error in his estimate of mean ignition duration will not exceed 0.01 seconds? c) A sample of 100 shoppers chosen at random from all shoppers in a given province indicated that 55% of them preferred a particular store (Shoprite). i. Find a 95% confidence interval for the proportion of all the shoppers that preferred Shoprite. ii. How large a sample of shoppers should we take in order to be 95% confident that the shoppers will buy from Shoprite? d) A sample of 150 Samsung phone batteries showed a mean lifetime of 1400 hours and a standard deviation of 120 hours. A sample of 200 i-phone batteries showed a mean lifetime of 1200 hours and a standard deviation of 80 hours. Find a 95% confidence interval for the difference of the mean lifetimes of the Samsung batteries and i-phone batteries.
Q3
a) A sample of 10 measurements of the radius of a marble gave a mean of 4.38mm and a
standard deviation of 0.06mm. Find a 99% confidence interval for the actual radius.
b) In measuring ignition duration, an engineer estimates that the standard deviation is 0.05
seconds. How large a sample of measurements must he take in order to be 95% confident
that the error in his estimate of mean ignition duration will not exceed 0.01 seconds?
c) A sample of 100 shoppers chosen at random from all shoppers in a given province
indicated that 55% of them preferred a particular store (Shoprite).
i. Find a 95% confidence interval for the proportion of all the shoppers that
preferred Shoprite.
ii. How large a sample of shoppers should we take in order to be 95% confident that
the shoppers will buy from Shoprite?
d) A sample of 150 Samsung phone batteries showed a mean lifetime of 1400 hours and a
standard deviation of 120 hours. A sample of 200 i-phone batteries showed a mean
lifetime of 1200 hours and a standard deviation of 80 hours. Find a 95% confidence
interval for the difference of the mean lifetimes of the Samsung batteries and i-phone
batteries.
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