Question

The policy of a particular bank branch is that its ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. At this branch the expected average amount of money withdrawn from ATM machines per customer transaction over the weekend is $220. Suppose that a random sample of 64 customer transactions is examined and it is observed that the sample mean withdrawal is $225 with sample standard deviation of $30. Using a 10% significance level, determine if there is evidence to suggest that the mean amount of money withdrawn from ATM machine per customer transaction over the weekend is greater than $220.

(a) Determine the null and alternative hypotheses

(b) decide on a significance level

(c) Compute the test statistic

(d) Find the P-value

(e) Decide whether or not to reject the null hypothesis by the P-value approach. Explain your reasoning.

(f) Interpret your results.

Please help me answer this question

Answer 1

(a)

Let the population mean amount of money withdrawn from ATM machine per customer transaction over the weekend be denoted by . The null and alternative hypotheses are given by

(b)

The significance level is given to be 10% i.e. 0.1

(c)

The given data are summarized as

n=64

s=30

The test statistic is given by

(d)

The p-value is obtained as

0.093617

(e)

As the p-value is less than 0.1, we reject the null hypothesis at 10% level of significance.

(f)

Hence it can be concluded that the population mean amount of money withdrawn from ATM machine per customer transaction over the weekend is greater than 220 at 10% level of significance.

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