Fall 2010 Practice Test 1 Key 1 For any set of data values the corresponding z scores standardized values always have a mean of 0 2 Joe scored 82 on an English exam where the mean score was 70 and the standard deviation was 6 while Jim scored 90 on a history exam where the mean was 80 and the standard deviation was 4 Find the standardized score for a Joe b Jim Who performed better Jim He was further above the mean for his group than Joe was for his group 3 Find the mean and standard deviation for the following numerical values Show all your work for the mean 2 3 4 7 9 mean 2 3 4 7 9 5 25 5 5 standard deviation from your calculator 2 915 as a sample 2 608 as a population 4 Consider the following set of numerical values 18 19 21 22 22 23 24 26 28 31 32 34 41 58 a Give the 5 number summary Find the values for the upper and lower fences and identify any outliers Minimum 18 Q1 22 Median 25 Q3 32 Maximum 58 IQR 32 22 10 Upper fence Q3 1 5 IQR 32 1 5 10 47 58 is an outlier Lower fence Q1 1 5 IQR 22 1 5 10 7 No further outliers b Draw a modified boxplot showing any outliers with a 5 True or False T If a collection of data is nearly symmetric the mean and median will be close to each other F All positive data values have positive z scores T The third quartile is also the 75th percentile T For a picture to be a true representation for a set of data the picture should satisfy the area principle F A pie chart is a special recipe for making flaky pie crusts 6 Classify each variable as quantitative or qualitative categorical For those that are quantitative tell whether it is continuous or discrete quantitative discrete the number of puppies in a litter qualitative the class standing freshman sophomore etc of a college student quantitative continuous the daily high temperature 7 T or F F For any set of data values the corresponding z scores always have a mean of 1 T For bell shaped data about 95 of the data values fall within two standard deviations of the mean F For data that is skewed to the right the median will be greater than the mean 8 The following sets of data have correlation coefficients of 768 504 971 and 1 You need to match the correct correlation with each graph A r 0 504 B r 0 971 C r 0 768 D r 1 9 Indicate whether you think the following association between the given variables would be positive negative or neither The mpg and weight of a car negative The height and shoe size of a woman positive 10 True or false F It is possible to have a correlation coefficient of 1 5 F A positive correlation indicates that the y values decrease as the x values increase T The slope of a line gives the amount the y value rises or falls when x increases by one unit T The y intercept of a line gives the y value when x 0 F If the correlation between explanatory variable x and response variable y is 1 this means that x causes y Fill in the blank The correlation coefficient measures the strength of the LINEAR association between two variables 11 From a set of data relating the value of a particular type of used cars it is found that model is years where and the linear is the value of the value of the car in dollars and is the age of the car in a What percentage of the variation of the data points is accounted for by the linear model 90 b What value would the linear model predict for a two year old car 17 400 c Suppose that one of the cars was actually two years old and its value was 17 000 Find the residual for that data point 400 d Explain the significance of the slope of the regression line That is what does it say about the value of the car The slope is 1300 year so the value of the car is predicted to decrease by 1300 per year 12 Consider the following fitted line plots Each one has an unusual point Indicate whether or not the unusual point is an outlier and whether the linear relationship would be strengthened or weakened by removing the unusual point A B C Outlier Y N Yes Yes Yes Strengthened or Weakened S W W S S 13 A small liberal arts university has 1000 students of which 300 are freshmen 300 are sophomores 200 are Junior and 200 are seniors An administrator wants to choose a sample of 100 students to do a survey Indicate the sampling technique used in each case a All the students are required to live in a dormitory complex on campus where all the students live in suites with 5 students in each suite The administrator chooses 20 suites at random and interviews all the students in each suite Cluster sample b Instead of a sample of size 100 the administrator surveys all 1000 students census c The administrator lists all the students by class and then randomly chooses 30 freshmen 30 sophomores 20 juniors and 20 seniors Stratified sample d The administrator lists all the students and uses a random number generator to select 100 numbers between 1 and 1000 and uses the students whose names are in those positions on the list SRS 14 True or False T For the regression line the sum of the residuals is always 0 F If the linear model is a good fit for the data points then the residual plot should have a pattern that is fairly linear T The regression line for the z scores always has a slope equal to the correlation coefficient F If a data point lies above the regression line then its residual is negative F The residuals always have a standard deviation of 1 F The correlation coefficient is affected by the units used F We can do correlation coefficients for categorical data T The regression line is the line for which the sum of the squares of the residuals is the smallest F The sum of the residuals is always zero regardless of the line used F Internet polls are a good source of statistically sound data