Math

StatisticsQ&A LibraryDefine 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 recorded4.ValuesFrequency39.312Based on these 75 observations, is a binomial distribution an appropriate model? Perform agoodness-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.)Question

Asked Mar 4, 2019

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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:

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:*

*H*_{0} : The binomial distribution is an appropriate model for the data.

*Alternative hypothesis:*

*H*_{1} : 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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