Math 364 Exam Two Review Questions

 

  1. A botanist wants to determine the population of tulip bulbs of a particular type that will bloom. He selects a random sample of 100 such bulbs and finds that 36 of them bloom.
    1. Calculate a 95% confidence interval for this proportion.

     

     

  2. Suppose a researcher wishes to conduct a survey of people to determine their attitude about success. Of the 100 randomly selected persons, 70 persons thought they were successful.
    1. What is the estimate of the percent of persons who felt they were successful?

       

    2. What is the SE in percent for your estimate?

       

    3. For the percent of persons who felt that they were successful, what is the chance or probability that the percentage is between 65% and 75%?

     

  3. A large sample found that the average height for males 17-23 years is 69 inches with SD = 3 inches and their average weight is 180 lbs with SD = 20 lbs. Correlation coefficient for these values is 0.6. We want to predict weight from a known height.
    1. What is the value of the slope?

       

    2. What is the value of the y-intercept?

       

    3. What is the expected value for the weight of a 21 year old man with a height of 75 inches?

       

    4. What is the RMS error?

     

  4. To determine the type of camera to buy, a consumer decided to perform a simple linear regression on the two variables that had the largest correlation coefficient, r = .82. The consumer collected data on 59 cameras that is summarized below:

     

    scatter 
    Regression Analysis


The regression equation is
clsup = - 7.32 + 10.5 typ

Predictor        Coef       StDev          T        P
Constant       -7.317       3.357      -2.18    0.033
typ           10.4826      0.9691      10.82    0.000

S = 10.12       R-Sq = 67.2%     R-Sq(adj) = 66.7%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1       11972       11972    116.99    0.000
Residual Error    57        5833         102
Total             58       17805

Unusual Observations
Obs        typ      clsup         Fit   StDev Fit    Residual    St Resid
 29       4.00      11.00       34.61        1.53      -23.61       -2.36R 
 30       4.00      11.00       34.61        1.53      -23.61       -2.36R 
 33       4.00      11.00       34.61        1.53      -23.61       -2.36R 
 38       4.00      55.00       34.61        1.53       20.39        2.04R 
 46       4.00      55.00       34.61        1.53       20.39        2.04R 
 47       4.00      55.00       34.61        1.53       20.39        2.04R 

R denotes an observation with a large standardized residual

Predicted Values for x = 2

     Fit  StDev Fit         95.0% CI             95.0% PI
   13.65       1.75   (   10.15,   17.15)  (   -6.91,   34.20)

     

    1. What is the relationship of camera type and close up?

       

    2. What is the explanatory variable?

       

    3. What is the response variable?

       

    4. What is the value of variable close up when camera type = 2?

       

    5. Is this prediction extrapolation?

       

    6. How much variation in close up is accounted for by camera type?

       

    7. What is the Standard Error of the estimated regression?

       

    8. What is the regression equation?

     

  5. What is the standard deviation of this box: {1 0 1 0 1 1}.

     

  6. One hundred draws will be made at random with replacement from the box: { 1 3 3 5 }.
    1. What is the expected value of the sum?

       

    2. The standard deviation of this box is 1.414, what is the standard error of the sum?

       

    3. The smallest sum is _______; the largest sum is ________.

       

    4. What is the chance that the sum is between 300 and 325?

     

  7. How many tosses would be better to have equal amounts of heads and tail? 10 tosses or 100 tosses.

     

  8. What are the five variables that define a scatter plot?

     

  9. What values of r (correlation coefficient) show the strongest correlation?

     

  10. A multiple choice test has 30 questions. There are five answers to choose. One is correct. What is the students score if the student randomly guesses at each question?

     

  11. What is the SEM if the SD = 42 and n = 60?

     

  12. What is the definition of the mean or average of a list of numbers?

     

  13. what is the definition of the standard deviation of a list of numbers?

     

  14. Who coined the term regression effect?

     

  15. On any day, a salesperson will sell 2 cars with a 15% chance, 1 car with a 30% chance, and no cars with a 55% chance. Over 20 sales days per month, how many cars will this person sell? Setup a box model and give the EV and SE of the sales total.