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    A High Street Bank is reviewing the operation of its cash machines. One of the problems the Bank faces is to ensure that the cash machines are stocked with enough cash to satisfy customers making withdrawals over an entire weekend. If too much cash is unnecessarily kept in the machines, the bank is forgoing the opportunity of investing the money and earning interest.

    Suppose that at a particular branch the population mean amount of money withdrawn from the cash machines per customer transaction over the weekend has been found to be £160 with a known population standard deviation of £30. Recent evidence suggests, however, that the mean amount may have changed. To test whether this is the case, a random sample of 36 customer transactions were examined and the sample mean was found to be £172. Assume that the amount of money withdrawn follows a normal distribution.

    a) Is there evidence to suggest that the population mean is no longer £160? Use a 0.05 level of significance. Compute the p-value and interpret its meaning
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    (Original post by dshot20)
    A High Street Bank is reviewing the operation of its cash machines. One of the problems the Bank faces is to ensure that the cash machines are stocked with enough cash to satisfy customers making withdrawals over an entire weekend. If too much cash is unnecessarily kept in the machines, the bank is forgoing the opportunity of investing the money and earning interest.

    Suppose that at a particular branch the population mean amount of money withdrawn from the cash machines per customer transaction over the weekend has been found to be £160 with a known population standard deviation of £30. Recent evidence suggests, however, that the mean amount may have changed. To test whether this is the case, a random sample of 36 customer transactions were examined and the sample mean was found to be £172. Assume that the amount of money withdrawn follows a normal distribution.

    a) Is there evidence to suggest that the population mean is no longer £160? Use a 0.05 level of significance. Compute the p-value and interpret its meaning
    You may wish to look up hypothesis testing and p-values in a standard statistical textbook. TSR policy is that you attempt the question first before asking for help.

    The link below is a graduate level text which deals with the subject matter, I can't think of any off the top of my head which are suitable for A-Level study, I'm sorry.

    http://www.statlect.com/hypothesis_testing_mean.htm

    I hope this helps.

    Darren
 
 
 
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