For each of the following scenarios, identify: • the population(s) of interest;

Question

For each of the following scenarios, identify:

• the population(s) of interest;

• the variable(s) being measured on each observational unit; if there are two variables, identify which is the explanatory variable and which is the response variable;

• whether the variable(s) being measured is categorical or quantitative;

• the parameter of interest, both in words and using the appropriate statistical symbol (p, p1 p2, µ, µ1 µ2, or µd); and

• the null and alternative hypotheses, written in correct statistical notation (not in words).

(a) Residents of a neighborhood have been complaining about speeding cars. The speed limit in the area is 25 miles per hour. The local police monitor the situation by recording the speed of 100 randomly selected cars. They want to know if cars that drive through the area drive faster than 25 miles per hour on average.

(b) Refer again to part (a). After collecting the data described in part (a), the police decide to install an electronic roadside sign that shows cars how fast they are driving. They then record the driving speed of another 100 randomly selected cars. They want to know whether the average speed is lower after installation of the sign than it was beforehand.

(c) At the beginning of the quarter, a professor surveyed her students and asked the question, ”Where do you typically sit in a classroom?” Possible responses were Front, Middle and Back. The professor hypothesized that the majority of students prefer to sit in the middle of the room.

Explanation / Answer

a) Residents of a neighborhood have been complaining about speeding cars. The speed limit in the area is 25 miles per hour. The local police monitor the situation by recording the speed of 100 randomly selected cars. They want to know if cars that drive through the area drive faster than 25 miles per hour on average.

population of interesting : Residents of a neighborhood

variable(s) being measured on each observational unit : The speed limit in the area

variable : categorical

symbol : miu

(b) Refer again to part (a). After collecting the data described in part (a), the police decide to install an electronic roadside sign that shows cars how fast they are driving. They then record the driving speed of another 100 randomly selected cars. They want to know whether the average speed is lower after installation of the sign than it was beforehand.

population of interesting : Residents of a neighborhood

variable(s) being measured on each observational unit : The speed limit in the area

variable : categorical

symbol : miu1 - miu2

(c) At the beginning of the quarter, a professor surveyed her students and asked the question, ”Where do you typically sit in a classroom?” Possible responses were Front, Middle and Back. The professor hypothesized that the majority of students prefer to sit in the middle of the room.

population of interesting : her students

variable(s) being measured on each observational unit : Where do you typically sit in a classroom?

variable : quantitaive

symbol : p ( proportions)

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