Question

Q1:

Let’s say our research question we want to find the average (mean) wage among all workers in the United States. Let’s say (and this is obviously not a very good method) we go around UC and stop 500 people and ask them what their wage is and calculate the mean wage.

• What is our population?
• What is our sample?
• What is the parameter?
• What is the statistic?
• What are some problems with our sampling method?

Q2:

Identify the scale of measurement: nominal, ordinal, interval, ratio

• Zip codes
• Stock prices
• Item size (small, medium, large)
• Income of households, measured in dollars
• Educational level, recorded as (High School, some college, college graduate)
• Test score (0-100), measuring score on first statistics exam
• Test score (0-100), measuring overall knowledge of statistics
• A video game was previewed to a group of 30 teenagers. The teens were asked to rate the quality of the graphics.

Q3

A paper manufacturer in Country A sells much of its paper in Country B. The manufacturer is paid in Country​ B's dollars, but pays its employees in Country​ A's dollars. The manufacturer is interested in the fluctuating exchange rate between these two currencies. Each trading day in 2005 the exchange rate fluctuated by several basis points.​ (A basis point is 1/100 of a​ percent.) A year of data is collected.

• Identify whether the data are cross sectional or a time series.
• Give a name to each variable and indicate if the variable is​ categorical, ordinal, or numerical​ (if a variable is​ numerical, include its units if​ possible)
• List any concerns that you might have for the accuracy of the data. Select all that apply.

1. The recorded exchange rates might not be accurate for 2005.
2. The fluctuations of the exchange rate in 2005 might not be typical of other years.
3. The exchange rate is dependent on the country in which the data is recorded.
4. There are no concerns regarding the accuracy of the data.

Q4: A bakery is trying to decide what makes a loaf a bread sell. There are three locations of this bakery and they gather data at all three locations. They measure the volume of the loaf and whether or not it has nuts in it. They then time how long it takes the loaf to sell. What are the cases? (unit of observation) List the variables and the scale of measurement

Q5:

• Why is the median not an acceptable measure for nominal data?

• Why is the mean not an acceptable measure for ordinal data?

• In a strongly skewed distribution, would you prefer the mean or the median?

Q6:

Clara asked twenty-one people what their favorite number is. Please calculate the most complex yet appropriate measure of central tendency for the following data:

7, 3, 0, 7, 8, 2, 1, 2, 7, 6, 10, 6, 7, 1, 10, 0, 6, 8, 10, 3, 1

Answer 1

1)a) Population is the group on which the information is to be found. Here the population is all workers of United States.

b)Sample is the smaller group of the population which is selected to represent the population. it would be a part of the population. The results vary according to the sample chosen. Sample is the 500 people we stopped in UC to ask the wages.

c)parameter is the characteristic of the population on which data is studied. it could be age, job nature etc. Here the Parameter is mean wage of workers in US.

d)Statistic is the characteristic of population, the same way as the parameter is to population. Here it is the mean wage of 500 people of UC.

e)The problems with the sampling method is that it is concentrated to UC only. The results would vary because the mean wage in UC might be higher or lower than rest of the US. A method to collect the sample would have been to collect it from different states of US, even if not all, based on the living standards etc.

2) Zip code: Nominal (not ordinal because there is no ranking)

Stock prices: Ratio

Item size: Ordinal (Small, medium and large)

Income of Households: Ratio

Education level:Ordinal because based on ranking like school, high school etc

Test score in first exam: ratio (because could be zero)

Test score overall: Ratio

Video games quality of graphics: ordinal

(You can comment for doubts)