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Question 1 Packets of instant coffee have a nominal weight of 32 grams. A random sample of 10 packets were selected and each of their weights, x grams, was recorded. It is found that: ∑▒x=305 , ∑▒x^2 =9505 (a) Find the unbiased estimate for the population mean and standard deviation. (3 marks) (b) A consumer association claimed that the mean weight of the instant coffee packet is less than 32 grams. Test at 5% significance level if this claim is true. (8 marks) Question 2 The efficiency of two training centres in a large organisation is to be evaluated. The examination results of a group of students from each centre on a common test are: Centre X Y Sample Size 50 40 Sample Mean 82.5 77 Sample Standard Deviation 7.2 9.1 Test at 1% level of significance, whether there is a significant difference in examination results between centres. (8 marks)
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