Question

Restaurants usually have more customers closer to Saturday than earlier in the week. A restaurant chain hypothesizes that, of all the customers in a week, only 8% come in on each of the 4 days, Sunday through Wednesday, whereas 21% come in on Thursday, 25% on Friday, and 30% on Saturday. The restaurant collects data over a random sample of days and obtains the following customer count. Management want to test the hypothesis that the distribution of customers over the days of the week is as they expect. Sunday-100 Monday-130 Tuesday-125 Wednesday-130 Thursday-310 Friday-370 Saturday-410 (a) Construct the table of expected frequencies. (b) Write the null and alternative hypotheses. State the requirements and verify whether they are met. (c) Suppose we reject the null hypothesis. Write the verbal conclusion in context.

Answer 1

(a)

Question:

Construct the table of expected frequencies.

Day of the week	Expected Frequency
Sunday	1575 X 8/100 = 126
Monday	1575 X 8/100 = 126
Tuesday	1575 X 8/100 = 126
Wednesday	1575 X 8/100 = 126
Thursday	1575 X 21/100 = 330.75
Friday	1575 X 25/100 = 393.75
Saturday	1575 X 30/100 = 472.5

(b)

(i)

Question:

Write the null and alternative hypotheses.

Answer:
H0: Null Hypothesis: the distribution of customers over the days of the week is as they expect. (Claim)

HA: Alternative Hypothesis: the distribution of customers over the days of the week is not as they expect.

(ii)

Question:

State the requirements and verify whether they are met.

The requirements are:

(1) The sampling method is Simple Random Sampling

(2) The variable under study is categorical

(3) The expected value of the number of sample observations in each level of the variable is at least 5.

It is verified that they are met.

(c)

Question:

Suppose we reject the null hypothesis. Write the verbal conclusion in context.

Answer:
If we reject the null hypothesis, we conclude as follows:
The data do not support the claim that the distribution of customers over the days of the week is as they expect.