In: Statistics and Probability

The Mean Corporation has been commissioned to conduct a study is into the relationship between the population of a city and the number of motor vehicle accidents in the city per year. A linear regression model is to be constructed. In the proposed regression model, number of motor vehicle accidents per year is the response variable and population of the city is the explanatory variable.

A random sample of 20 cities is selected and measurements are observed.

Population ('000s) |
No. accidents per year |
---|---|

3,480 | 7,117 |

1,670 | 4,344 |

2,280 | 5,576 |

1,310 | 4,356 |

1,530 | 5,115 |

2,540 | 5,692 |

1,630 | 4,348 |

1,090 | 3,092 |

1,660 | 4,166 |

980 | 3,912 |

1,560 | 3,355 |

2,210 | 5,471 |

3,490 | 7,419 |

1,650 | 4,756 |

3,190 | 7,050 |

2,020 | 5,209 |

2,810 | 6,451 |

3,140 | 6,919 |

1,830 | 3,889 |

420 | 2,273 |

**a)**Calculate the point prediction for the value x =
1,000. Give your answer as a whole number.

y^ =

**b)**Give the 95% prediction interval for the value x
= 1,000. Give your answers as whole numbers.

≤ y^ ≤

The statistical software output for this problem is:

Hence,

a) Predicted value = **3377**

b) 95% prediction interval:

**2394** < y < **4361**

Professor Galant has been conducting a
study on the relationship between happiness and chocolate
consumption.
In her study, she selects 15 caouples pairs and
evaluates the change in happiness, on a scale of 1 to 100, after
eating a chocolate bar
She hired you as a statistical
consultant. Analyze these data and draw the most
reasonable conclusion(s)
What scientific question(s) are you trying to
answer?
What statistical method(s) have you used, and
why?
List your null hypotheses and alternate hypotheses,
if any....

You have been asked to study whether there is a statistical
relationship between the region of the country and the categorical
number of stores that have experienced at least a 20% return rate
of the item you are studying. Sample data concerning these two
variables is given in appendix three. At both the 5% and 2% levels
of significance, is there evidence of a relationship between the
region of the country and the categorical number of stores that
have experienced...

3) You have been asked to study whether there is a statistical
relationship between the region of the country and the categorical
number of stores that have experienced at least a 20% return rate
of the item you are studying. Sample data concerning these two
variables is given in appendix three. At both the 5% and 2% levels
of significance, is there evidence of a relationship between the
region of the country and the categorical number of stores that
have...

The US Postal Service has recently commissioned a study of the
effects of 3d printing on its business. Some were pessimistic,
saying 3d printing would be bad for the postal service, while
others were optimistic, saying that 3d printing would be a boom to
the postal service. Why do you suppose informed people could hold
such divergent views?

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
6
13
15
34
Science Fiction
14
11
5
30
Comedy...

The relationship between "strength" and "fineness" of cotton
fibers was the subject of a study that produced the following data.
(Give your answers correct to two decimal places.)
x, Strength
76
69
71
76
83
72
78
74
80
82
y, Fineness
4.3
4.7
4.7
4.0
4.1
4.0
4.8
4.7
4.3
4.5
(b) Find the 98% confidence interval for the mean measurement of
fineness for fibers with a strength of 70.
Lower Limit
Upper Limit
(c) Find the 98% prediction...

The relationship between "strength" and "fineness" of cotton
fibers was the subject of a study that produced the following data.
(Give your answers correct to two decimal places.)
x, Strength
76
69
71
76
83
72
78
74
80
82
y, Fineness
4.3
4.5
4.7
4.0
4.1
4.2
5.0
4.9
4.3
4.3
(a) Draw a scatter diagram. (Do this on paper. Your instructor
may ask you to turn in this work.)
(b) Find the 95% confidence interval for the mean...

The following data was collected during a study to determine if
there is a relationship between the vertical drop of the mountain
and the number of trails at the resort in New York State. (1200,
30), (700, 50), (700, 24), (1500, 62), (1010, 23), (3350, 67),
(400, 15), (1600, 34) a.) Generate the regression equation. b.)
Determine the correlation coefficient. c.) Is there enough evidence
to conclude that the slope of the regression line is not zero at
the 98%...

The relationship between "strength" and "fineness" of cotton
fibers was the subject of a study that produced the following data.
(Give your answers correct to two decimal
places.)
x, Strength
75
78
74
69
80
82
80
86
70
88
y, Fineness
3.8
4
4.5
3.7
4.3
3.8
3.8
4.7
4.8
3.7
(a) Find the 98% confidence interval for the mean measurement of
fineness for fibers with a strength of 76.
Upper Limit -
Lower Limit-
(b) Find the 99%...

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
9
18
7
34
Science Fiction
10
12
8
30
Comedy...

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