1. A salesperson makes four calls per day. A sample of 100 days gives the follow
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Question
1. A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.
Number of Sales
Observed Frequency (Days)
0
30
1
40
2
20
3
8
4
2
Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. Assume that the population has a binomial distribution with n = 4, p =.25, and x = 0, 1, 2, 3, and 4.
a. Compute the expected frequencies for x = 0, 1, 2, 3, and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.
b. Use the goodness of fit test to determine whether the assumption of a binomial distribution should be rejected. State the Hypotheses and the conclusion. Use = .10. Note: Because no parameters of the binomial distribution were estimated from the sample data, the degrees of freedom are k-1 where k is the number of categories.
Please tell me exactly what to type into Excel to get these answers and if any formulas could be used to get them. Thank you
Number of Sales
Observed Frequency (Days)
0
30
1
40
2
20
3
8
4
2
Explanation / Answer
null hypothesis: distribution follows a binomial distribution with n = 4, p =.25
alternate hypothesis:distribution does not follow a binomial distribution with n = 4, p =.25
here for each categories proportion can be calculated by formula binomdist(x,4,0.25,false)
like for category 0 number of sales ; corresponding proportion p=binomdist(0,4,0.25,false)=0.3164
applying chi square goodness of fit on above:
as expected frequency in 3 and 4 number of sales are lower then 5; we will add these to recalculate our table values:
from above test stat X2 =5.0256
and degree of freedom =(number of categories -1)=3
hence p value =chidist(5.0256,3)=0.1699
as p value is greater then 0.10 level we can not rject null hypothesis that above distribution follows binomial with parameter n=4 and p=0.25.
observed Expected Chi square number of sales Probability O E=total*p =(O-E)^2/E 0 0.3164 30.000 31.64 0.09 1 0.4219 40.000 42.19 0.11 2 0.2109 20.000 21.09 0.06 3 0.0469 8.000 4.69 2.34 4 0.0039 2.000 0.39 6.63 1 100 100 9.2267Related Questions
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