A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.Number of SalesX0120314234TotalObserved FrequencyRecords show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial probability distribution. The binomial probability function presented in Chapter 5 isf(x) =n!x!(n-x)!*p*(1 − p)^ - *.ExpectedFrequencies(days)For this exercise, assume that the population has a binomial probability distribution with n = 4, p = 0.30, 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.30x = 2x = 3O x = 4Onone of the above332836100Do any of the categories have an expected frequency that is less than five? (Select all that apply.)Ox=0Ux=1 Before conducting a goodness of fit test, we must combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories. What categories should we combine in order to satisfy this requirement?O x = 3 and x = 4O x = 2 and x = 3O x = 0 and x = 1O x = 0, x = 1, and x = 3O We don't need to combine any categories.(b) Use the goodness of fit test to determine whether the assumption of a binomial probability distribution should be rejected. Use a = 0.05. Because no parameters of the binomial probability distribution were estimated from the sample data, the degrees of freedom are k-1 when k is the number of categories.State the null and alternative hypotheses.O Ho: The population does not have a binomial distribution.H₂: The population has a binomial distribution.O Ho: The sample does not have a binomial distribution.H₂: The sample has a binomial distribution.O Ho: The population has a binomial distribution.H₂: The population does not have a binomial distribution.OH: The sample has a binomial distribution.H₂: The sample does not have a binomial distribution.Find the value of the test statistic. (Round your answer to three decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.O Reject Ho. We conclude that the assumption of a binomial distribution can be rejected.O Reject Ho. We conclude that the assumption of a binomial distribution cannot be rejected.O Do not reject Ho. We conclude that the assumption of a binomial distribution can be rejected.O Do not reject Ho. We conclude that the assumption of a binomial distribution cannot be rejected.

Let X be the random variable that no. of sales. The observed frequencies are given as, x O 0 30…

Answered: (b) Use the goodness of fit test to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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