Question

Question 1

Amanda, a local supermarket owner, has decided to use a more analytical approach to improve her store's customer service. Her goal is to maintain the ratio of people working in the store over the number of customers around 1.5. What this means is, for example, for every two customers at any point in time there would be three people working at the store.

In order for her to achieve this ratio, she wants to re-evaluate her knowledge about the number of people entering the store at any given time in a more analytical way. She knows based on her experience on average 1 customers enter the store every 30 mins. To verify this assumption, she has recorded the customer's foot traffic for 5 hours.

Using the information she has recorded in the table below, please calculate the upper and lower bound for a 90% confidence interval mean of recorded sample.

Hours | #Customers |
---|---|

9am-9.30am | 3 |

9.30am-10am | 1 |

10am-10.30am | 1 |

10.30am-11am | 3 |

11am-11.30am | 1 |

11.30am-12pm | 3 |

12pm-12.30pm | 3 |

12.30pm-1pm | 4 |

1pm-1.30pm | 1 |

1.30pm-2pm | 3 |

90% Confidence interval lower bound

Round your answer to 1 decimal place (ex.: 19.4 for 19.432).

90% Confidence interval upper bound

Round your answer to 1 decimal place (ex.: 19.4 for 19.432).

------------------------------------------------------------------------------------

Question 2

Using the information that Amanda's captured during the 5 hours, run a hypothesis testing to check if the average number of customers per 30 min is greater than 1 customers per 30 min.

?0: The average number of customers per 30 min is not greater than 1

?1: The average number of customers per 30 min is greater than 1

What is the test statistics of this hypothesis testing?

Round your answer to 1 decimal place (ex.: 19.4 for 19.432).

Based on a significance level of 10%, can we reject the null hypothesis?

Round your numbers to 1 decimal place (ex.: 19.4 for 19.432).

------------------------------------------------------------------------------------

Question 3

Considering the column "#Item Purchased" represents the corresponding number of items that were purchased in-store during each time window, what is the correlation between the number of customers entering the store and the number of purchased items?

Hours | #Customers | #Item Purchased |
---|---|---|

9am-9.30am | 3 | 5 |

9.30am-10am | 1 | 1 |

10am-10.30am | 1 | 2 |

10.30am-11am | 3 | 5 |

11am-11.30am | 1 | 2 |

11.30am-12pm | 3 | 6 |

12pm-12.30pm | 3 | 7 |

12.30pm-1pm | 4 | 6 |

1pm-1.30pm | 1 | 1 |

1.30pm-2pm | 3 | 3 |

What is the correlation value between number of customers entering the store and number of purchased items?

Round your numbers to 1 decimal place (ex.: 19.4 for 19.432).

------------------------------------------------------------------------------------

Question 4

If X and Y are random variables with negative correlation. Which of the following are correct?(select all that apply)

A) If we observe higher than average values of X, we expect to see higher than average values of Y

B) X and Y are independent variables with negative covariance

C) If we observe higher than average values of X, we expect to see lower than average values of Y

D) X and Y are dependent variables with negative covariance

Answer #1

Question 1

**90% Confidence interval lower bound = 1.6**

**90% Confidence interval upper bound = 3.0**

2.300 | mean Data |

1.160 | std. dev. |

0.367 | std. error |

10 | n |

9 | df |

1.6 | confidence interval 90.% lower |

3.0 | confidence interval 90.% upper |

0.7 | margin of error |

Question 3

What is the correlation value between number of customers entering the store and number of purchased items?

**0.9**

Question 4

**C) If we observe higher than average values of X, we
expect to see lower than average values of Y**

**D) X and Y are dependent variables with negative
covariance**

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