Homework 2 (30 points)
STAT 210
Name(s) ____SOLUTION_____
Due: Tuesday, September 18th by 4pm
1. According to genetic theory, the blossom color in the second generation of a certain cross of
sweet peas should be red ¾ of the time and white the other ¼ of the time. Suppose a
researcher from the University of Nebraska was interested in engineering a breed of sweet pea
that blossomed red more than ¾ of the time (Go Big Red! ). The researcher developed the
new breed of sweet pea seed and planted 80 of them. Of the 80 seeds planted, 68 had red
blossoms.
Research Question – Is there evidence that the new breed of sweet pea seeds blossoms
red more often than the previous breed?
a. Define the population of interest. (1 point)
All sweet pea seeds
b. Define the variable of interest. (1 point)
Blossom Color
c. Describe in context how this follows a binomial distribution. (5 points)
1.
2.
3.
4.
n = 80 seeds
Red Blossom, White Blossom
P(Red Blossom) = 0.75 for each seed
Seeds are independent of one another
d. Assuming ¾ of sweet pea blossoms bloom red, how many of the 80 seeds planted would
you expect to bloom red? (1 point)
80(0.75) = 60
e. Create the binomial distribution for this scenario using JMP. What values do you need
to use for n and p? You do not need to include your JMP output. (2 points)
n = 80
f.
p = 0.75
Assuming ¾ of sweet pea blossoms bloom red, what is the probability of observing
results at least as extreme as was observed? Use the distribution you created in part e
to answer this question. (2 points)
P(X ≥ 68) = 0.0221
g. Does this study provide evidence that the researcher successfully created a breed of
sweet peas that bloom red more often? Explain. (3 points)
Evidence (p-value = 0.0221) that the new breed of sweet pea seed blooms red
more often than the previous breed.
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2. An internet retail business is trying to decide whether to pay a search engine company to
upgrade its advertising. In the past, 15% of customers who visited the company’s webpage by
clicking through on an advertisement bought something. If the business decides to purchase
premium advertising, then the search engine company will make that company’s ad more
prominent. The search engine company offers to do an experiment: For one day customers will
see the retail business’s ad in the more prominent position. The retail business can then decide
whether the advertising improves the percentage of purchases made by click throughs. The one
day trial resulted in 300 click throughs, 54 of which resulted in a purchase.
Research Question – Did the premium advertising increase the percent of customers
who clicked through and bought something?
a. Define the population of interest. (1 point)
All customers
b. Define the variable of interest. (1 point)
Click through purchase status
c. Describe in context how this follows a binomial distribution. (5 points)
1.
2.
3.
4.
n = 300 customers
Click through purchase, No click through purchase
P(click through purchase) = 0.15 for each customer
Customers are independent of one another
d. Assuming 15% of click throughs result in a purchase, how many of the 300 people would
you expect to make a purchase? (1 point)
300(0.15) = 45
e. Create the binomial distribution for this scenario using JMP. What values do you need
to use for n and p? You do not need to include your JMP output. (2 points)
n = 300
f.
p = 0.15
Assuming 15% of click throughs result in a purchase, what is the probability of observing
results at least as extreme as was observed? Use the distribution you created in part e
to answer this question. (2 points)
P(X ≥ 54) = 0.0870
g. Does this study provide evidence that prominent advertising increases the percent of
click throughs resulting in a purchase? Explain. (3 points)
No evidence (p-value = 0.0870) that premium advertising increases the
number of click through purchases.
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