Question 1

Sweet potato pie Sam is preparing sweet potato pies as his dessert for Thanksgiving. The store he shops at sells six sweet potatoes in a bag. He has found that each bag will contain
0, 1, or 2 bad sweet potatoes. Based on experience he estimates that there will be no bad sweet potatoes in 40% of the bags, one bad sweet potato in 30% of the bags, and two bad sweet potatoes in the rest. Conduct a simulation to estimate how many bags Sam will have to purchase to have three dozen sweet good potatoes.
a. Describe how you will use a random number table to conduct this simulation.
b. Show two trials by clearly labeling the random number table given below. Specify the outcome for each trial. $\begin{array}{|c|cc|c|}
\hline \text { Trial } &{\text { Simulation }} && \text { Outcome } \
\hline{\# 1} & 578821 & 76309 & \
\hline & 635508 & 29418 & \
\hline{\# 2} & 133026 & 34993 & \
\hline & 54636 & 17877 & \
\hline
\end{array}$ 
c. State your conclusion.

Accepted Answer

a. Use the digits 0-3 to represent bags with 6 good sweet potatoes (none bad), digits
4-6 to represent bags with five good sweet potatoes (one bad), and digits 7-9 to
represent bags with four good sweet potatoes (two bad). Look at each single digit of the random number table to determine whether you have 4, 5, or 6 good sweet potatoes in the bag. Continue this until the cumulative count is at least 36 good sweet potatoes.
b. Show two trials by clearly labeling the random number table given below. Specify the outcome for each trial. $\begin{array}{|c|c|c|}
\hline \text { Trial } & \text { Simulation } & \text { Outcome } \\hline
\#1&\begin{array}{lll}&5&7&8&2&1&\quad\quad&7&6&3&0&9\
\text { \# good: }&5&4&4&6&6&&4&5&6\
\text { Total good: }&5&9&13&19&25&&29&34&40\\hline&6&3&5&0&8&&2&9&4&1&8
\end{array}&\begin{array}{lll}
\text { Need to purchase } 8 \text { bags }\\text { to get at least three }\\text { dozen good sweet }\\text { potatoes. }
\end{array}\
\hline \#2&\begin{array}{lll}&1&3&0&2&6&&3&4&9&9&3\
\text { \# good: }&6&6&6&6&5&&6&5\\text { Total good: }&6&12&18&24&29&&35&40\
\hline&5&4&6&3&6&&1&7&8&7&7
\end{array}&\begin{array}{lll}
\text { Need to purchase } 7 \text { bags }\\text { to get at least three }\\text { dozen good sweet }\\text { potatoes. }
\end{array}\
\hline
\end{array}$ c. According to my simulation, it will take (on average) 7.5 bags of sweet potatoes to get at least three dozen good sweet potatoes for the pies.

Question 2

A factory has 20 assembly lines producing a popular toy. To inspect a representative sample of 100 toys, quality control staff randomly selected 5 toys from each line's output. Was this a simple random sample?

Accepted Answer

A)   Yes, because the toys were selected at random.
B)   Yes, because each toy produced had an equal chance to be selected.
C)   No, because toys do not come off the assembly line at random.
D)   No, because not all combinations of 100 toys could have been chosen.
E)   Yes, because a stratified sample is a type of simple random sample. D

Question 3

Political math A recent study by Yale professors found that people's ability to do mathematics computations got worse when the result went against the person's political ideology. This was based on a randomized experiment in which people were given the same basic computation, but some were given the question in a politically neutral context and others were given the same computation in a context in which the correct answer went against their political ideology. The difference between the proportion of people who got the question wrong in a 'neutral' context and those who got the question wrong in a
'political' context was reported to be "statistically significant."
a. Briefly explain what "statistically significant" means in this context.
b. Would it be appropriate for the news media to report that the political context caused the
poor computational results? Explain.

Accepted Answer

a. The difference in computational correctness was greater than random variation might reasonably be expected to produce.
b. This was a randomized experiment, so it is appropriate to assert that the political context caused the difference in computational correctness.

Question 4

A group of people are concerned that the coach of a local high school men's and women's basketball teams alters the amount of air in the basketball to gain an unfair advantage over opponents during home games. The idea is that the basketballs are pumped up with one pound per square inch less air than required, and his teams practiced with these altered balls all week prior to home basketball games. Since these under-pumped basketballs would react differently to being shot at a basket, the team that practiced with these balls would have an unfair advantage when it came to shooting free throws.
-Describe how to use a prospective study to determine if the home teams have an unfair advantage when shooting free-throws.

Accepted Answer

The answer of A group of people are concerned that...

Question 5

We wish to compare the average ages of the math and science teachers at your school. Which is the best way to collect the data?

Accepted Answer

A)   experiment
B)   simulation
C)   census
D)   observational study
E)   sample survey

Question 6

Twenty dogs and 20 cats were subjects in an experiment to test the effectiveness of a new flea control chemical. Ten of the dogs were randomly assigned to an experimental group that wore a collar containing the chemical, while the others wore a similar collar without the chemical. The same was done with the cats. After 30 days the veterinarians were asked to inspect the animals for fleas and evidence of flea bites. This experiment is...

Accepted Answer

A)   completely randomized with one factor: the species of animal
B)   randomized block, blocked by species
C)   randomized block, blocked by type of collar
D)   completely randomized with two factors
E)   completely randomized with one factor: the type of collar

Question 7

Max wants to start a farm to grow mussels. He needs to determine the best environment for growing them. He is going to try two different amounts of salt in the water (salinity) and three different water temperatures. For his experiment he has
18 aquariums, each with 20 mussels. He wants to see which environment produces the largest mussels.
-Identify the subjects.

Accepted Answer

The answer of Max wants to start a farm to...

Question 8

Max wants to start a farm to grow mussels. He needs to determine the best environment for growing them. He is going to try two different amounts of salt in the water (salinity) and three different water temperatures. For his experiment he has
18 aquariums, each with 20 mussels. He wants to see which environment produces the largest mussels.

-Identify the treatments.

Accepted Answer

The answer of Max wants to start a farm to...

Question 9

Which is important in designing a good experiment?
I. Randomization in assigning subjects to treatments.
II. Control of potentially confounding variables.
III. Replication of the experiment on a sufficient number of subjects.

Accepted Answer

A)   II and III
B)   I only
C)   I and II
D)   I, II, and III
E)   I and III

Question 10

A tree farmer hires a botanist to evaluate a blight that seems to be affecting his trees. The trees are planted in horizontal rows on a hill and the blight seems to be a bigger problem near the bottom of the hill. The farmer wants to know the extent of the damage to the trees. Since the trees must be destroyed to examine them, the botanist doesn't have time to examine all the trees, so she will select a sample. Several plans for choosing the sample are proposed. Name the sampling strategy in each.
a. Randomly select three trees from each  orizontal row.
b. Lay out a grid on a map of the hill. Randomly select eight squares from the grid, and check all trees in those squares.
c. Randomly pick a number from 1 to 30. Start at the tree at that position in the first row,then go to every 30th tree after that.
d. Check the ten trees closest to the parking lot where the botanist parks her car.

Accepted Answer

The answer of A tree farmer hires a botanist to...

Question 11

A researcher wants to compare the effect of a new type of shampoo on hair condition. The researcher believes that men and women may react to the shampoo differently. Additionally, the researcher believes that the shampoo will react differently on hair that is dyed. The subjects are split into four groups: men who dye their hair; men who do not dye their hair; women who dye their hair; women who do not dye their hair. Subjects in each group are randomly assigned to the new shampoo and the old shampoo. This experiment

Accepted Answer

A)   has one factor (shampoo type) , blocked by gender and whether hair is dyed.
B)   is completely randomized.
C)   has two factors (gender and whether hair is dyed)  blocked by shampoo type.
D)   has two factors (shampoo type and whether hair is dyed)  blocked by gender.
E)   has three factors (shampoo type, gender, whether hair is dyed) .

Question 12

In order to see which variety of apple tree produces more fruit, a farmer sets up an experiment. He has three plots of land with different soil and natural water availability. Each plot has room for eight trees. The farmer randomly selects four locations in each plot for the first variety of tree and the other four get the second variety. This experiment is...

Accepted Answer

A)   randomized block, blocked by plot of land
B)   completely randomized with one factor: the plot of land
C)   completely randomized with two factors
D)   randomized block, blocked by variety of tree
E)   completely randomized with one factor: the variety of tree

Question 13

On January 1 of every year, many people watch the Rose Parade on television. The week before the parade is very busy for float builders and decorators. Roses, carnations, and other flowers are purchased from around the world to decorate the floats. Based on past experience, one float decorator found that 10% of the bundles of roses delivered will not open in
time for the parade, 20% of the bundles of roses delivered will have bugs on them and be unusable, 60% of the bundles of roses will turn out to be beautiful, and the rest of the bundles of roses delivered will bloom too early and start to discolor before January 1. Conduct a simulation to estimate how many roses the float decorator will need to purchase to have 15
good bundles of roses to place on the float.

-Describe how you will use a random number table to conduct this simulation.

Accepted Answer

The answer of On January 1 of every year, many...

Question 14

Among a dozen eggs, three are rotten. A cookie recipe calls for two eggs; they'll be selected randomly from that dozen. Which plan could be used to simulate the number of rotten eggs that might be chosen?
I. Let 0, 1, and 2 represent the rotten eggs, and 3, 4, …, 11 the good eggs. Generate two random Numbers 0-11, ignoring repeats.
II. Randomly generate a 0, 1, or 2 to represent the number of rotten eggs you get.
III. Since 25% of the eggs are rotten, let 0 = rotten and 1, 2, 3 = good. Generate two random v numbers 0-3 and see how may 0's you get.

Accepted Answer

A)   I or III only
B)   III only
C)   II only
D)   I, II, or III
E)   I only

Question 15

Which of the following is not required in an experimental design?

Accepted Answer

A)   control
B)   replication
C)   blocking
D)   All are required in an experimental design.
E)   randomization

Question 16

Bone Builder Researchers believe that a new drug called Bone Builder will help bones heal after children have broken or fractured a bone. The researchers believe that Bone Builder will work differently on bone breaks than on bone fractures, because of differences in
initial bone condition. Bone Builder will be used in conjunction with traditional casts. To test the impact of Bone Builder on bone healing, the researchers recruit 18 children with bone breaks and 30 children with bone fractures. Design an appropriate experiment to
determine if Bone Builder will help bones heal.

Accepted Answer

The answer of Bone Builder Researchers believe that a new...

Question 17

A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next five free throw attempts?
I. Let 0,1 represent making the first shot, 2, 3 represent making the second shot,…, 8, 9 represent making the fifth shot. Generate five random numbers 0-9, ignoring repeats.
II. Let 0, 1, 2 represent missing a shot and 3, 4,…, 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9.
III. Let 0, 1, 2 represent missing a shot and 3, 4,…, 9 represent making a shot. Generate five random
Numbers 0-9 and count how many numbers are in 3-9, ignoring repeats.

Accepted Answer

A)   II and III
B)   I, II, and III
C)   I only
D)   II only
E)   III only

Question 18

Video games A headline in a local newspaper announced "Video game playing can lead to better spatial reasoning abilities." The article reported that a study found "statistically significant differences" between teens who play video games and teens who do not, with teens who play video games testing better in spatial reasoning. Do you think the headline was appropriate? Explain.

Accepted Answer

The answer of Video games A headline in a local...

Question 19

There are 1,237 trees on the hill. Explain how to use a random digit table to select a simple random sample of 20 trees. Then use the random digit table below to select the first five trees for your sample. 
$ \begin{array}{lllll}04905 & 8852 & 29350 & 91397 & 94531&78981&81980&08530\
19994&65142&05087&11232&39129&49559&94540&24070
\end{array} $

Accepted Answer

The answer of There are 1,237 trees on the hill....

Question 20

Name and describe the kind of bias that might be present if the statistics teacher decides that instead of randomly selecting students to survey on how they feel about the course she just…
a. asks students to volunteer for the survey. b. gives the survey during class one day.

Accepted Answer

The answer of Name and describe the kind of bias...

Exam 3: Displaying and Describing Categorical Data

A factory has 20 assembly lines producing a popular toy. To inspect a representative sample of 100 toys, quality control staff randomly selected 5 toys from each line's output. Was this a simple random sample?

We wish to compare the average ages of the math and science teachers at your school. Which is the best way to collect the data?

Which is important in designing a good experiment? I. Randomization in assigning subjects to treatments. II. Control of potentially confounding variables. III. Replication of the experiment on a sufficient number of subjects.

Which of the following is not required in an experimental design?

Name and describe the kind of bias that might be present if the statistics teacher decides that instead of randomly selecting students to survey on how they feel about the course she just… a. asks students to volunteer for the survey. b. gives the survey during class one day.