A type of new car is offered for sale with 4 option packages. A customer can buy any number of​ these, from none to all 4. A manager proposes the null hypothesis that customers pick packages at​ random, implying the number of packages bought by a customer should be binomial with n=4. This table shows the number of packages chosen by 300 customers. ​(a) Find the binomial parameter p needed to calculate the expected counts. ​(b) Find the estimated probability that a customer picks one option. ​(c) Find the degrees of freedom for χ2. ​(d) Find the value of χ2 for testing H0. ​(e) Find the​ p-value for testing H0 Packages Customers   0 23   1 80   2 117   3 78   4 2 ​(a) The binomial parameter p is   ​(Round to three decimal places as​ needed.)

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A type of new car is offered for sale with 4 option packages. A customer can buy any number of​ these, from none to all 4. A manager proposes the null hypothesis that customers pick packages at​ random, implying the number of packages bought by a customer should be binomial with
n=4.
This table shows the number of packages chosen by
300
customers.
​(a) Find the binomial parameter p needed to calculate the expected counts.
​(b) Find the estimated probability that a customer picks one option.
​(c) Find the degrees of freedom for
χ2.
​(d) Find the value of
χ2
for testing
H0.
​(e) Find the​ p-value for testing
H0
Packages
Customers
 
0
23
 
1
80
 
2
117
 
3
78
 
4
2
​(a) The binomial parameter p is
 
​(Round to three decimal places as​ needed.)
Expert Solution
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Since you have posted a question with multiple sub-parts, we will solve the first three subparts for you. To get the remaining sub-parts solved please repost the complete question and mention the sub-parts to be solved.

a) parameter p is the probability of picking a number of packages at random.

Total no of packages is given to be = 4

So, the sample space of the event of selecting a number of packages by customers will be-

{0, 1, 2, 3, 4}

There are a total of 5 outcomes, so the probability of anyone of the above outcomes occurring is given by 15=0.2

Hence, p = 0.2

b) Let X be the no of packages bought by customer.

To calculate P[X=1]

Therefore,

PX=1=410.211-0.24-1               =410.20.83               =0.4096

 

 

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