Question

A fine dining restaurant claims that the group sizes of their customers follow the following distribution: 2 people, 3 people, 4 people, 4+ people - 36%, 12%, 17%, 35%. Gustavo, a waiter at the restaurant, would like to test this claim. He takes a sample of 92 customers and records the observed frequencies in the following table: 2 people - 35, 3 people - 10, 4 people - 24, 4+ people - 23.

(a) In performing this statistical test, state the hypotheses.
H0: The distribution of customers for each group is the same as claimed by the restaurant.
HA: The distribution of customers for each group is not the same as claimed by the restaurant.

(b) What are the expected frequencies of each group? Fill out the table. (Round your answers to 2 decimal places, if needed.)
2 people - 33.12, 3 people - 11.04, 4 people - 15.64, 4+ people - 32.20

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.)
TS = 2.41

Answer 1

The question is about conducting a hypothesis test to determine whether the observed customer group sizes at a restaurant match the claimed distribution. Hypotheses are stated, expected frequencies are calculated based on the sample size, and the test statistic is provided as 2.41.

Step-by-step explanation:

The question involves conducting a hypothesis test to compare the observed group sizes at a fine dining restaurant with the group sizes that the restaurant claims. Gustavo, the waiter, observes a sample of 92 customers and wants to test the claim about their distribution.

Part (a): State the Hypotheses

Null Hypothesis (H0): The distribution of customer group sizes is the same as the claim made by the restaurant.
Alternative Hypothesis (HA): The distribution of customer group sizes is not the same as the claim made by the restaurant.

Part (b): Expected Frequencies

To calculate the expected frequencies, the sample size is multiplied by the claimed percentages for each group size:

2 people: 92 customers x 36% = 33.12

3 people: 92 customers x 12% = 11.04

4 people: 92 customers x 17% = 15.64

4+ people: 92 customers x 35% = 32.20

Part (c): Test Statistic Value

The test statistic (TS) is calculated based on the observed frequencies and the expected frequencies. The provided test statistic value is 2.41.