The policy of a particular bank branch is that its ATMs must be stocked with eno

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. Customer goodwill depends on such services meeting customer needs. At this branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160 with a population standard deviation of $30. Suppose that a random sample of 36 customer transactions is examined, and you find that the sample mean withdrawal amount is $172.

a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence to believe that the population mean withdrawal amount is greater than $160? b. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence to believe that the population mean withdrawal amount is greater than $160?

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Explanation / Answer

a ) The critical z-value corresponding to an upper tail probability of 0.05 is 1.645.

1.645 = (x^ - u) / s/sqrtn

1.645 = x- 160 / 30 /sqrt36

1.645=x-160 /5

8.225= x-160

x= 168.225

The critical value is 168.225. sample mean is greater than 168.225,

then we will reject the null hypothesis.

In this case, our sample mean of 172 is greater then the critical value,

so we reject the null hypothesis and can say that the true mean is greater than $160.

b) zo = x- u / (s/sqrtn)

   = 172-160/( 30/sqrt36)

   = 2.4

z value corresponds to a probability of 0.4918.

This implies a one-tailedp-value of 0.5 – 0.4918 = 0.0082.

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