The Chi-Square test for Population Variance
The Chi-Square [pic]test for Population Variance[pic]
Recall that we used the [pic] distribution in constructing the confidence interval for normally distributed population variance[pic]. This distribution is also used to test a claim about the variance or standard deviation.
To find the area under the chi-square distribution, use textbook Table 6 page 832. There are three cases to consider:
Let’s Do It 1
1. Finding the chi-square critical value for a specific a when the hypothesis test is right-tailed. [pic]
[pic]
2. Finding the chi-square critical value for a specific a when the hypothesis test is left-tailed. [pic]
[pic]
3. Finding the chi-square critical values for a specific a when the hypothesis test is two-tailed. [pic]
[pic]
[pic]
[pic]
Example
A cigarette manufacturer wishes to test the claim that the variance of nicotine content of its cigarettes is 0.644. Nicotine content is measured in milligrams and is assumed normally distributed. A sample of 20 cigarettes has a standard deviation of 1.00milligram. At [pic], is there enough evidence to reject the manufacturer’s claim?
Step 1: State the hypotheses and identify the claim.
[pic]
Step 2: Find the critical values. Since this test is a two-tailed test at[pic]. The critical values for 0.025 and 0.975 must be found. The degrees of freedom are 19; hence, the critical values are 32.852 and 8.907, respectively. The critical regions are shown in Figure below
Step 3: Compute the test value. [pic]
Since the standard deviation s is given in the problem, it must be squared for the formula.
Step 4: Make the decision. Do not reject the null hypothesis, since the test value falls between the critical values region, as shown below
[pic]
Step 5: Summarize the results. There is not enough evidence to reject the manufacturer’s claim that the variance of the nicotine content of the cigarettes is equal to 0.644.
Let’s Do It 2
A nutritionist claims that the variance of the number of calories in 1tbs of the major brands of pancake syrup is greater than 3600. A sample of 18 major brands of syrup yielded a variance of 4175. Test this claim assuming the number of calories is normally distributed.
Let’s Do It 3
In a study in which the subjects were 15 patients suffering from pulmonary sarcoid disease, blood gas determinations were made. The variance of the sample was 450. Test the hypothesis that the population variance is less than 250.
Let’s Do It 4
A nutritionist claims that the standard deviation of the number of calories in 1 tablespoon of the major brands of pancake syrup is 60. A sample of major brands of syrup is selected, and the number of calories is shown. At [pic]= 0.10, can the claim be rejected?
53 210 100 200 100 220
210 100 240 200 100 210
100 210 100 210 100 60
Homework page 285: 42, 43, 45
-----------------------
The Decision Tool (THE TEST STATISTIC)
In order to perform the hypothesis test, we first determine the distribution of the test statistic used in performing the test.
The test statistic for population variance is
[pic]
Hypothesis-Testing Problems (Traditional Method)
Step1: State The null and the Alternative and identify the claim.
Step2: Find the critical value(s) from the appropriate table.
Step3: Compute the test statistic.
Step 4: Summarize the results. Note: Never accept the null. We reserve the judgment about the hypothesis is true.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- 08 probability threory binomial distribution
- 00 psy221 title and cover page fayetteville state university
- standard deviation 物理系
- california state university northridge
- the chi square test for population variance
- how to calculate median mode mean variance and
- chapter 6 variance and standard deviation
- variance and standard deviation information
- how to calculate variance and standard deviation
Related searches
- t test for population mean calculator
- pearson chi square analysis
- chi square analysis in excel
- chi square calculator
- chi square excel template
- chi square made simple
- chi square critical value calculator
- chi square analysis
- chi square calculator in excel
- chi square calculator ti 84
- chi square critical value table
- chi square distribution in excel