Question

A bank manager claims that the median number of customer per day is no more than 440. A teller doubts the accuracy of this claim. The number of bank customers per day for 16 randomly selected days are listed below

410, 416, 416, 420, 430, 433, 437, 440, 450, 455, 455, 460, 463, 465, 465, 470

At the 0.05 significance level, test the bank manager's claim.

The test statistic x is______

The x-critical value is________

Answer 1

hypothesis:-

here we are doing sign test for median.

necessary calculation table:-

put a + sign if the value is > 440

put - sign if the value is < 440

put 0 if the value = 440

days	sign
410	-
416	-
416	-
420	-
430	-
433	-
437	-
440	0
450	+
455	+
455	+
460	+
463	+
465	+
465	+
470	+

total number of + sign (X⁺) = 8

total number of - sign (X^-)= 7

n = total number of + sign (X⁺) + total number of - sign (X^-)= 8+7 =15

the test statistic x is = 7

[ min (X⁺, X^-) = 7]

the x critical value is(X^*) = 3

[ for n = 15, alpha= 0.05, one tailed test ]

decision:-

so, we fail to reject the null hypothesis.

we conclude that,

At the 5% level of significance, we can not reject the bank manager’s claim that the median number of customers per day is no more than 440.

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