(a) A machine is used to fill soft drink in bottles. 35 randomly selected bottles
are taken from the output of the machine. Those bottles have a mean
volume of 330 ml with a standard deviation of 4.8 ml. Construct a 98%
confidence interval to estimate the true mean volume of soft drink.
(5 marks)
(b) The marketing department of a smart phone store is interested in
determining the proportion of new smart phone owners who would have
spent more than or equal to RM 2000 to buy a new smart phone. Suppose
that a survey of 45 new customers, 23 indicate that they would have
purchased new smart phone which cost more than or equal to RM2000.
Construct a 99% confidence interval for the true proportion of new smart
phone owners who have spent more than or equal to RM2000 for a new
smartphone. (5 marks)
(a) The critical value for and degrees of freedom is
The corresponding confidence interval is computed as shown below:
Therefore, based on the data provided, the 98% confidence interval for the population mean is which indicates that we are 98% confident that the true population mean is contained by the interval
(b) The sample proportion is computed as follows, based on the sample size and the number of favorable cases
The critical value for is
The corresponding confidence interval is computed as shown below:
Therefore, based on the data provided, the 99% confidence interval for the population proportion is which indicates that we are 99% confident that the true population proportion is contained by the interval
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