Question
Asked Mar 4, 2019
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Define Yas the number of under-filled bottles from a filling operation in a carton of 24 bottles.
Of 75 cartons inspected, the following observations on X were recorded
4.
Values
Frequency
39
.3
12
Based on these 75 observations, is a binomial distribution an appropriate model? Perform a
goodness-of-fit procedure with a -0.05.
a)
b) Calculate the P-value for this test. (The R command chisq.test can get a specific value.)
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Define Yas the number of under-filled bottles from a filling operation in a carton of 24 bottles. Of 75 cartons inspected, the following observations on X were recorded 4. Values Frequency 39 .3 12 Based on these 75 observations, is a binomial distribution an appropriate model? Perform a goodness-of-fit procedure with a -0.05. a) b) Calculate the P-value for this test. (The R command chisq.test can get a specific value.)

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Expert Answer

Step 1

Given information:

Denote the variable “number of under filled bottles from a filling operation of 24 bottles” as X.

The data represents the number of under filled bottles from a filling operation of 24 bottles among the 75 inspected cartons.

The specific probabilities for the variable “number of under filled bottles from a filling operation of 24 bottles” are given below:

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Step 2

a.

Perform a goodness of fit procedure to test whether binomial distribution is an appropriate model for the data or not:

State the appropriate hypothesis.

The hypotheses are given below:

Null hypothesis:

H0 : The binomial distribution is an appropriate model for the data.

Alternative hypothesis:

H1 : The binomial distribution is not an appropriate model for the data.

Step 3

Obtain the test statistic value.

Here, MINITAB software is used to find the test statistic.

Software procedure:

Step by step procedure to obtain the test statistic using the MINITAB software:

  • Choose Stat > Tables > Chi-square goodness of fit (One variable).
  • In Observed counts enter the column of Frequency.
  • In Category names enter the column of
  • In Test select Specific proportions and enter the column of
  • In Sample1 enter Trea...
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