Question

Bobo's bad burgers fast food claims you will be in and out in 5 mins. To test this claim, time in mins from entering Bobo's to receiving the order was secretly recorded. The results: 2.1 8 4.6 2.5 3.5 4.3 3.9 5 6.5 3.4 5.6 6.6 4.3 4.9 9.3 5.5 4.3 11.9 5.2 4.8 5.2 7.8 8 4.6 4 5.9 8.7 3.1 4.9 11.6 2.1 8 4.6 2.5 3.5 4.3 3.9 5 6.5 3.4 5.6 6.6 4.3 4.9 9.3 5.5 4.3 11.9 5.2 4.8 5.2 7.8 8 4.6 4 5.9 8.7 3.1 4.9 11.6 At 95% confidence level, does the confidence interval support Bobo's claim?

Answer #1

Here we need to find a 95% confidence interval to check whether the confidence interval supports Bobo's claim.

Before we go on to construct the confidence interval let us know
a bit about **t-test and the construction of the confidence
interval.**

**Coming back to our
problem,**

Given that Bobo's bad burgers fast food claims you will be in and out in 5 mins and to test this claim, time in mins from entering Bobo's to receiving the order was secretly recorded. The data is,

No. | Time in mins(xi) | (xi-x̄)^2 |

1 | 2.1 | 12.72111 |

2 | 8 | 5.444444 |

3 | 4.6 | 1.137778 |

4 | 2.5 | 10.02778 |

5 | 3.5 | 4.694444 |

6 | 4.3 | 1.867778 |

7 | 3.9 | 3.121111 |

8 | 5 | 0.444444 |

9 | 6.5 | 0.694444 |

10 | 3.4 | 5.137778 |

11 | 5.6 | 0.004444 |

12 | 6.6 | 0.871111 |

13 | 4.3 | 1.867778 |

14 | 4.9 | 0.587778 |

15 | 9.3 | 13.20111 |

16 | 5.5 | 0.027778 |

17 | 4.3 | 1.867778 |

18 | 11.9 | 38.85444 |

19 | 5.2 | 0.217778 |

20 | 4.8 | 0.751111 |

21 | 5.2 | 0.217778 |

22 | 7.8 | 4.551111 |

23 | 8 | 5.444444 |

24 | 4.6 | 1.137778 |

25 | 4 | 2.777778 |

26 | 5.9 | 0.054444 |

27 | 8.7 | 9.201111 |

28 | 3.1 | 6.587778 |

29 | 4.9 | 0.587778 |

30 | 11.6 | 35.20444 |

31 | 2.1 | 12.72111 |

32 | 8 | 5.444444 |

33 | 4.6 | 1.137778 |

34 | 2.5 | 10.02778 |

35 | 3.5 | 4.694444 |

36 | 4.3 | 1.867778 |

37 | 3.9 | 3.121111 |

38 | 5 | 0.444444 |

39 | 6.5 | 0.694444 |

40 | 3.4 | 5.137778 |

41 | 5.6 | 0.004444 |

42 | 6.6 | 0.871111 |

43 | 4.3 | 1.867778 |

44 | 4.9 | 0.587778 |

45 | 9.3 | 13.20111 |

46 | 5.5 | 0.027778 |

47 | 4.3 | 1.867778 |

48 | 11.9 | 38.85444 |

49 | 5.2 | 0.217778 |

50 | 4.8 | 0.751111 |

51 | 5.2 | 0.217778 |

52 | 7.8 | 4.551111 |

53 | 8 | 5.444444 |

54 | 4.6 | 1.137778 |

55 | 4 | 2.777778 |

56 | 5.9 | 0.054444 |

57 | 8.7 | 9.201111 |

58 | 3.1 | 6.587778 |

59 | 4.9 | 0.587778 |

60 | 11.6 | 35.20444 |

Total |
340 |
338.6133 |

Here we need to **find a 95% confidence interval for
μ.**

where **c is the confidence coefficient,**

Since **confidence coefficient c=0.95,**

Now,

Now t values with 59 degrees of freedom are not provided in the Biometrika Tables so here we use normal approximation to approximate the values of the t-distribution. Now this approximation is fairly good if n>30.

Now here,

Therefore the **confidence interval for μ** is,

**Lower,**

**Upper,**

Hence the **95% confidence interval for μ is given by
(5.0392,6.2942).**

**Since 5 min is not within the confidence interval the
confidence interval does not support Bobo's claim.**

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