A fine dining restaurant claims that the group sizes of their customers follows the following distribution:

2 people 3 people 4 people 4+ people

33% 10% 19% 38%

Gustavo, a waiter at the restaurant, would like to test this claim. He takes a sample of 97 customers and records the observed frequencies in the following table:

2 people 3 people 4 people 4+ people

34 0 23 40

(a) In performing this statistical test, state the hypotheses.

H0: the distribution of customers for each group is not the same as the observed frequencies vs. HA: the distribution of customers for each group is the same as the observed frequencies

H0: the distribution of customers for each group is the same as the observed frequencies vs. HA: the distribution of customers for each group is not the same as the observed frequencies

H0: the distribution of customers for each group is the same as claimed by the restaurant vs. HA: the distribution of customers for each group is not the same as claimed by the restaurant

H0: the proportions of customers for each group are all the same vs. HA: the proportions of customers for each group are not all the same

H0: the distribution of customers for each group is not the same as claimed by the restaurant vs. HA: the distribution of customers for each group is the same as claimed by the restaurant

(b) What is the expected frequencies of each group? Fill out the table. (Round your answers to 2 decimal places, if needed.)

2 people3 people4 people4+ people

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

TS=

(d) The test statistic follows achi-square distribution with df = 4

chi-square distribution with df = 96

t-distribution with df = 4

chi-square distribution with df = 3

t-distribution with df = 3

.

(e) Using the statistical table, the p-value is0.005 < p-value < 0.01

0.01 < p-value < 0.025

0.025 < p-value < 0.05

p-value > 0.10

0.05 < p-value < 0.10

0 < p-value < 0.005

.

(f) Based on the p-value, those conducting the test should areject bfail to reject the null hypothesis at the significance level of 0.05.

(g) What is the appropriate conclusion?

There is sufficient evidence to conclude the proportions of customers for each group are not all the same.

There is sufficient evidence to conclude the distribution of customers for each group is the same as claimed by the restaurant.

There is insufficient evidence to conclude the distribution of customers for each group is not the same as claimed by the restaurant.

There is sufficient evidence to conclude the distribution of customers for each group is not the same as claimed by the restaurant.

There is insufficient evidence to conclude the proportions of customers for each group are not all the same.