Question

_____ 14. Determine the expected count under the null hypothesis.

A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level.

Monday Tuesday Wednesday Thursday Friday Total

Number Served 40 33 35 32 60 200

Provided the assumptions of the test are satisfied, determine the expected number of customers served each day under the null hypothesis.

a) 20

b) 25

c) 30

d) 40

e) 50

Answer 1

Notice here, that under the null hypothesis, we assume that, the local retailer serves the customers Uniformly throughout the week.

i.e.

Under Ho :- The data is Uniformly Distributed.

Now, we have to obtain the Expected number of customers served under Ho, the null hypothesis.

We know that, Expected Frequency, Ei= n*pi

Since, we have 5 weekdays... Hence.

We have , pi= 1/5

And it is given that, total is 200

Hence, n= 200

So, using, n=200 and ,p=1/5

We get , Expected Frequency,

Ei = n * pi = 200 *(1/5) = 40

Hence, Ei= 40

Therefore, the Expected number of customers served under the null hypothesis Ho are

D)40

This answers your question.

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