24% of all the M&Ms produced are blue M&Ms | Complete Solution

For each quantity in boldface Questions 1-4 ask you to determine which is a parameter and which is a statistic.
 

Question 1
24% of all the M&Ms produced are blue M&Ms - but in a small package of M&M's I found only 12%.
A.        A.    24% is a statistic and 12% is also a statistic
B.        B.    24% is a statistic and 12% is a parameter
C.        D.    24% is a parameter and 12% is a parameter
E.        C. 24% is a parameter and 12% is a statistic
 
Question 2
In a recent poll Gallup found 51% of the adults they interviewed approved of the job President Obama has done in office. Of course, that is just an estimate of the percentage of all American adults who approved of the President's job in office.
A.        A)    51% is a statistic and the percentage of all American adults who approve of the President's job in office is also a statistic
B)        B)    51% is a statistic and the percentage of all American adults who approve of the President's job in office is a parameter
C)        D)    51% is a parameter and the percentage of all American adults who approve of the President's job in office is also a parameter
E)        C)    51% is a parameter and the percentage of all American adults who approve of the President's job in office is also a statistic
 
Question 3
513 is the average score on the SATM for all who have taken the SATM this past year while the average score for all men was 520.
A)        A) 513 is a statistic and 520 is also a statistic
B)        B)    513 is a statistic and 520 is a parameter
C)        D)    513 is a parameter and 520 is also a parameter
E)        C)    513 is a parameter and 520 is a statistic
 
Question 4
A recent poll by the Pew Research Center found that 66% of their respondents believed that education should be a top priority for Congress and the President. However this changed to 78% when you just looked at their female respondents.
A)        B)    66% is a statistic and 78% is also a statistic
C)        A)    66% is a statistic and 78% is a parameter
B)        C)    66% is a parameter and 78% is also a parameter
D)        D) 66% is a parameter and 78% is a statistic
    

The next set of questions ask about the normal approximation, when it applies and when it doesn't.

Question 5
A kitchen cabinet business has primarily homeowners as customers, but the business also has a few customers who are developers that build multi-unit condominiums. Overall, the average sale is $20,000, with a median sale of $10,000. Which of the following would be closest to a normal distribution?
A)        B)    the histogram of the next 50 individual sales
C)        A)    the histogram of the last 50 individual sales
B)        C)    the histogram of the average sales (sampling distribution) for random samples of size 5
D)        D)    the histogram of the average sales (sampling distribution) for random samples of size 40
 
Question 6
It is known that 5% (p = 0.05) of a particular brand of fuses is defective. Which of the following would be closest to a normal distribution (normal curve)?
    A)    the histogram of sample proportions of defective fuses for samples of size n =1
    B)    the histogram of sample proportions of defective fuses for samples of size n = 5
    C)    the histogram of sample proportions of defective fuses for samples of size n = 20
    D)    the histogram of sample proportions of defective fuses for samples of size n = 200
 
Question 7
For which of the following situations would the histogram of the sample mean (sampling distribution) look LEAST like a normal curve)?
A)        B)    A random sample of size 20 is drawn from a variable describing how many cigarettes had been smoked that day by individual students being studied.
C)        A)    A random sample of size 100 is drawn from a variable describing how many cigarettes had been smoked that day by individual students being studied.
B)        C)    A random sample of size 20 is drawn from a population of student grade point averages whose histogram looks very symmetric.
D)        D) A random sample of size 100 is drawn from a population of student grade point averages whose histogram looks very symmetric.

Multiple Choice Questions

Question 8
We are given that the average amount spent on textbooks by all incoming freshmen was $400 (μ) with a standard deviation of $25 (σ). The sampling distribution of the sample mean for randomly selected samples of 100 freshmen has a standard deviation of $2.50. Which of the following is the correct interpretation of the population standard deviation compared to the sampling distribution’s standard deviation?
    A)    The population standard deviation of $25 gives the variation in amount spent amongst all freshmen. The sampling distribution’s standard deviation of $2.50 gives the variation in the average amount spent amongst all samples of 100 freshmen.
    B)    The population standard deviation of $25 gives the variation in the average amount spent amongst all samples of 100 freshmen. The sampling distribution’s standard deviation of $2.50 gives the variation in amount spent amongst all freshmen.
 
Question 9
Forty percent (40% or 0.40, as a proportion) of all cars owned by residents of Lordstown, OH and the surrounding area are the Chevrolet brand. If a random sample of 81 car owners is selected in that area, then the sampling distribution of the sample proportion of those who own a Chevrolet brand car will be centered around 0.40 (40%) with a standard deviation of:
C)        A)    .09 or 9%
B)        B)    .054 or 5.4%
C)        D)    .946 or 94.6%
E)        C)    .049 or 4.9%
 
Question 10
A kitchen cabinet business has primarily homeowners as customers, but also has a few customers that are developers who build multi-unit condominiums. Overall, the average sale is $15,000, with a median sale of $10,000 and a standard deviation of $4,800. The standard deviation of the mean value for samples of 100 customers would be which of the following?
A)        B)    $4,800
C)        A)    $480
B)        C)    $48
D)        D)    $4.80
 

Question 11
Twenty percent (20%) of all students who live on campus at Penn State’s University Park campus have a car that they have registered to park in one of the University’s parking lots. You randomly select 100 students who live on campus and find that 24 of the 100 have a car registered to park in one of the University’s parking lots. What is the standard score (i.e. Z score) of your sample proportion?
A)        B)    +0.24
C)        A)    + 1.00
B)        C)    -1.00
D)        D)    -0.24
 
Question 12
Twenty percent (20%) of all students who live on campus at Penn State’s University Park campus have a car that they have registered to park in one of the University’s parking lots. You randomly select 100 students who live on campus and find that 18 of the 100 have a car registered to park in one of the University’s parking lots. What is the probability of having a sample proportion less than 0.18?
A)        B)    69%
C)        A)    31%
B)        C)    50%
D)        D)    95%
 
Question 13
The average monthly cell phone bill for all customers of a particular cell phone carrier in Pennsylvania is $85 with a standard deviation of $10. What is the standard score (Z score) for a random sample of 25 customers with an average amount spent monthly of $90?
A)        B)    +.50
C)        A)    - .50
B)        C)    +2.5
D)        D)    -2.5
 

Question 14
The average monthly cell phone bill for all customers of a particular cell phone carrier in Pennsylvania is $85 with a standard deviation of $10. What is the probability of obtaining a sample of size 25 that has a sample mean between $83 and $87?
A)        B)    90%
C)        A)    95%
B)        C)    68%
D)        D)    none of the above
 
Question 15
You flip a coin 5 times. Which of the following is the most likely pattern to observe (for example HHTHT means you get two heads then a tail then a head then a tail)
A)        B)    HHHHH
C)        A)    TTTTT
B)        C)    THTTH
D)        D)    all of the above have the same chance of happening

Question 16
Assume that Fifteen percent (15%) of all individuals in a particular city have Diabetes.  A hospital analyst studies the treatment records for two hospitals in that city for a particular day.   Hospital A treated 700 individuals that day, while Hospital B treated 300 individuals that day.
For which hospital is it more likely that between 10% and 20% of those treated had Diabetes?
A)        A) It is more likely among the 700 individuals treated in Hospital A.
B)        B)    It is more likely among the 300 individuals treated in Hospital B.
C)        C)    It is just as likely among either group of individuals.
 
Question 17
Assume that Fifteen percent (15%) of all individuals in a particular city have Diabetes.  A hospital analyst studies the treatment records for two hospitals in that city for a particular day.   Hospital A treated 700 individuals that day, while Hospital B treated 300 individuals that day.
Suppose that the first 20 individuals treated in Hospital A did not have Diabetes. What is the probability that the 21st individual treated in Hospital A will have Diabetes?
A)        B)    Still 15%
C)        A)    Higher than 15%
B)        C)    Lower than 15%
D)        D)    Not 15%, but could be higher or lower
 

Question 18
Fifteen percent (15%) of all individuals in a certain city have Diabetes.   If a random sample of 25 is selected from the city population, then the percentage of them with Diabetes will be around 15% give or take a standard deviation (spread of the sampling distribution) of:
A)        B)    7.1%
C)        A)    71%
B)        C)    14.2%
D)        D)    21.3%
 
Question 19
Overall, the selling prices for houses in a given county average $267,000 with a median of $165,000 and a standard deviation of $4,000.    Which of the following would be closest to a normal distribution (bell shaped curve)?
A)        A)The sampling distribution for the average of the next 30 selling prices
B)        B)A histogram of the next 30 selling prices
C)        C)A histogram of the last 30 selling prices
 
Question 20
Overall, the selling prices for houses in a given county average $267,000 with a median of $165,000 and a standard deviation of $4,000.     The standard deviation of the average selling price for the next 100 houses sold would be:
A)        B)    $400
C)        A)    $40,000
B)        C)    $4,000
D)        D)    $40
 
Question 21
Assume that ten percent (10%) of all individuals in a particular city have Diabetes.     You randomly select 100 individuals who live in the city and find that 13 of the 100 have Diabetes.    A sample proportion of 0.13 has a standard score (Z score) of +1.0.    What is the probability of having a sample proportion greater than 0.13?
A)        B)    0.16
C)        A)    0.84
B)        C)    0.90
D)        D)    0.68
E)        E)    0.95