31. ATMs must be stocked with enough cash to satisfy customers mananw is forgng

ID: 3316442 • Letter: 3

Question

31. ATMs must be stocked with enough cash to satisfy customers mananw is forgng he o satisfy customers making withdrawals over an entre of investing the money and earning interest. Suppose amount of money withdrawn from ATMs p Shis unnecessarily kept in the ATMs, the bank is forgoing the opportunity that at a particular branch the expectes mean er custo mer transaction over the weekend is $160 with standard deviation of $30. If withdrawal is $172, the which is what the average level of significance in a 6-step hypothesis test. a random sample of 36 customers is examined and the sample mean is there evidence to believe that the POP average withdrawal is no longer $160, re eviden p withdrawal is supposed to be according to past bank records? Use a 0.05

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Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 160
Alternative hypothesis: 160

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 5

DF = n - 1 = 36 - 1

D.F = 35
t = (x - ) / SE

t = 2.4

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 35 degrees of freedom is less than - 2.4 or greater than 2.4.

Thus, the P-value = 0.022

Interpret results. Since the P-value (0.022) is less than the significance level (0.05), we have to reject the null hypothesis.

Form the above test we have sufficient evidence in the favor of the claim that average wittdrawal is no longer 160.

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31. ATMs must be stocked with enough cash to satisfy customers mananw is forgng

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