Question

**PLEASE URGENT**

The restaurant owner Lobster Jack wants to find out what the peak demand periods are, during the hours of operation, in order to be better prepared to serve his customers. He thinks that, on average, 60% of the daily customers come between 6:00pm and 8:59pm (equally distributed in that time) and the remaining 40% of customers come at other times during the operating hours (again equally distributed). He wants to verify if that is true or not, so he asked his staff to write down during one week the number of customers that come into the restaurant at a given hour each day. His staff gave him the following data:

Time | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 |
---|---|---|---|---|---|---|---|

5:00pm-5:59pm | 15 | 19 | 21 | 20 | 12 | 15 | 15 |

6:00pm-6:59pm | 30 | 23 | 24 | 25 | 28 | 29 | 26 |

7:00pm-7:59pm | 36 | 29 | 39 | 35 | 39 | 30 | 32 |

8:00pm-8:59pm | 29 | 33 | 23 | 29 | 24 | 32 | 27 |

9:00pm-9:59pm | 21 | 20 | 12 | 19 | 18 | 14 | 20 |

10:00pm-10:59pm | 12 | 12 | 15 | 12 | 10 | 15 | 14 |

11:00pm-11:59pm | 8 | 7 | 9 | 10 | 12 | 12 | 9 |

Help the manager figure out if his instincts are correct or not. Use a Chi-Squared test to see if the observed distribution is similar to the expected. Use the average demand for a given time as your observed value.

**1. What is the p-value of your Chi-Square
test?**

**2. to test if his initial hypothesis is accurate at 80%
confidence interval. You set up the below Hypothesis
test**

**H0: The actual sales distribution resembles the expected
distribution at the 80% confidence level
H1: The actual sales distribution does not resemble the expected
distribution at the 80% confidence level
Which of the following is true?**

- We reject the Null Hypothesis.

- We cannot reject the Null Hypothesis.

- We cannot make any decision.

---

The owner now wants you to help him analyze his sales data. The restaurant is famous for its Lobo lobster roll. You were given some information based on which you deduced that the demand for the lobster roll was normally distributed with a mean of 220 and standard deviation of 50. You also know that the lobster supplier can provide lobster at a rate that mimics a uniform distribution between 170 and 300. One Lobster is used per roll and the lobsters need to be fresh (i.e. the restaurant can only use the lobsters that are delivered that day).

You decide to run 200 simulations of 1000 days each.

**1. Calculate the expected sales of Lobster roll per day
based on your simulation results.**

**2. Use the expected sales from each of your 200
simulations to create a confidence interval for the average
expected sales. What is the 95% confidence interval, L (Your
confidence interval is mean +/- L), for this estimate?**

Answer #1

Answer :-

Using matlab-

(1) Awhat is the p-value of your chi-square test?

Chi-square Test for the Association. Time, worksheet columns

Rows : Time columns : worksheet columns

person chi-square = 18.833, DF = 36, p-value = 0.992

Likelihood Ratio chi-square = 19.014, DF = 36, p-value = 0.991

p-value = 0.991

(2) Which of the following is true?

P-value > 0.2 (Alpha = 1 - 0.8 = 02.) So we v=cannot reh=ject the Null hypothesis.

Using matlab,

Part 1 : A- What is the p-value of your chi-square test?

chi- square test for association time, worksheet columns.

Row : Time Columns : Worksheet columns.

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