Download presentation

Presentation is loading. Please wait.

1
**Ch8 Inference concerning variance**

Dr. Deshi Ye

2
**Outline The estimation of variance Hypothesis concerning one variance**

Hypothesis concerning two variances

3
**One Population Tests One Population Mean Proportion Variance Z Test**

t Test Z Test c 2 Test (1 & 2 (1 & 2 (1 & 2 (1 & 2 tail) tail) tail) tail)

4
**8.1 The Estimation of Variances**

Standard deviation S Variance Let be the sample variance based on any population having variance

5
**Unbiased estimation of a population variance**

The sample variance is an unbiased estimator of Remark: the sample standard deviation S is not an unbiased estimator of However, for large samples the bias is small, and it is common practice to estimate with S

6
**Confidence interval By Theorem 6.4**

is a random variable having the chi-square distribution with n-1 degrees of freedom. 100(1-a)% confidence interval for

7
**8.2 Hypothesis concerning one variance**

Consider the problem of testing the null hypothesis that a population variance equals a specified constant against a suitable one-sided or two-sided alternative. Null Hypothesis is a random sample from a normal population with the variance is a random variable having the chi-square distribution with n-1 degree of freedom.

8
**Criterion Region for testing (Normal population)**

Alternative hypothesis Reject null hypothesis if

9
**EX. Testing hypothesis concerning a standard deviation**

The lapping process which is used to grind certain silicon wafers to the proper thickness is acceptable only if , the population standard deviation of the thickness of dice cut from the wafers, is at most 0.5 mil. Use the 0.05 level of significance to test the null hypothesis against the alternative hypothesis ,if the thickness of 15 dice cut from such wafers have a standard deviation of 0.64 mil.

10
**Solution 1. Null hypothesis: Alternative hypothesis**

2. Level of significance: 0.05 3. Criterion: Reject the null hypothesis if 4. Calculation: 5. The null hypothesis cannot be rejected at level 0.05. 6. P-value: = > level of significance

11
**8.3 Hypothesis concerning two variances**

If independent random samples of size and are taken from normal population having the same variance, it follows from Theorem 6.5 that is a random variable having the F distribution with and degrees of freedom

12
Testing two variances Null hypothesis

13
**Criterion Region for testing (Normal population)**

Alternative hypothesis Test statistic Reject null hypothesis if

14
EX. It is desired to determine whether there is less variability in the silver plating done by Company 1 than in that done by Company 2. If independent random samples of size 12 of the two companies’ work yield and , test the null hypothesis against the alternative hypothesis at the 0.05 level of significance.

15
**Solution 1. Null hypothesis: Alternative hypothesis**

2. Level of significance: 0.05 3. Criterion: Reject the null hypothesis if 4. Calculation: 5. The null hypothesis must be rejected at level 0.05. 6. P-value: =0.035 < level of significance

Similar presentations

OK

1/23 Ch10 Nonparametric Tests. 2/23 Outline Introduction The sign test Rank-sum tests Tests of randomness The Kolmogorov-Smirnov and Anderson- Darling.

1/23 Ch10 Nonparametric Tests. 2/23 Outline Introduction The sign test Rank-sum tests Tests of randomness The Kolmogorov-Smirnov and Anderson- Darling.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on mobile network layer Ppt on construction in maths Ppt on power line communication technology Ppt on statistics in maths games Ppt on depth first search java Ppt on low level language of computer Ppt on rational numbers for class 9 Ppt on various types of web browser Ppt on db2 introduction letter Ppt on kindness is contagious