CHAPTER 7 Tests of Hypotheses and Significance

QR Code 2d Barcode Reader In NoneUsing Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.

QR Code ISO/IEC18004 Encoder In NoneUsing Barcode maker for Software Control to generate, create QR Code 2d barcode image in Software applications.

(a) On the basis of a one-tailed test at a 0.01 level of significance, we would reject H0 if T were greater than t0.99, which, for n1 n2 2 12 12 2 22 degrees of freedom, is 2.51. Therefore, we cannot reject H0 at a 0.01 level of significance. (b) On the basis of one-tailed test at a 0.05 level of significance, we would reject H0 if T were greater than t0.95, which for 22 degrees of freedom is 1.72. Therefore, we can reject H0 at a 0.05 level of significance. We conclude that the improvement in yield of wheat by use of the fertilizer is probably significant. However before definite conclusions are drawn concerning the usefulness of the fertilizer, it may be desirable to have some further evidence. (c) The P value is P(T P 0.039. 1.85). The table in Appendix D shows 0.025 P 0.05. By computer software,

Quick Response Code Reader In NoneUsing Barcode scanner for Software Control to read, scan read, scan image in Software applications.

Printing QR In C#Using Barcode printer for .NET Control to generate, create QR Code JIS X 0510 image in Visual Studio .NET applications.

Tests involving the chi-square distribution 7.20. In the past the standard deviation of weights of certain 40.0 oz packages filled by a machine was 0.25 oz. A random sample of 20 packages showed a standard deviation of 0.32 oz. Is the apparent increase in variability significant at the (a) 0.05, (b) 0.01 level of significance (c) What is the P value of the test

QR Code Generation In Visual Studio .NETUsing Barcode encoder for ASP.NET Control to generate, create QR image in ASP.NET applications.

Draw QR Code In .NET FrameworkUsing Barcode encoder for .NET framework Control to generate, create QR Code image in .NET framework applications.

We have to decide between the hypotheses H 0: s H1: s The value of x2 for the sample is x2 0.25 oz and the observed result is due to chance 0.25 oz and the variability has increased ns2 >s2 20(0.32)2 >(0.25)2 32.8.

Generate QR Code In Visual Basic .NETUsing Barcode creator for .NET Control to generate, create QR-Code image in .NET applications.

Barcode Generator In NoneUsing Barcode generator for Software Control to generate, create barcode image in Software applications.

(a) Using a one-tailed test, we would reject H0 at a 0.05 level of significance if the sample value of x2 were greater than x2 , which equals 30.1 for n 20 1 19 degrees of freedom. Therefore, we would reject 0.95 H0 at a 0.05 level of significance. (b) Using a one-tailed test, we would reject H0 at a 0.01 level of significance if the sample value of x2 were greater than x2 ,which equals 36.2 for 19 degrees of freedom. Therefore, we would not reject H0 at a 0.01 0.99 level of significance. We conclude that the variability has probably increased. An examination of the machine should be made. (c) The P value is P(x2 P 0.0253. 32.8). The table in Appendix E shows 0.025 P 0.05. By computer software,

GTIN - 13 Printer In NoneUsing Barcode printer for Software Control to generate, create EAN 13 image in Software applications.

Print UPC Code In NoneUsing Barcode generation for Software Control to generate, create UPC Symbol image in Software applications.

Tests involving the F distribution 7.21. An instructor has two classes, A and B, in a particular subject. Class A has 16 students while class B has 25 students. On the same examination, although there was no significant difference in mean grades, class A had a standard deviation of 9 while class B had a standard deviation of 12. Can we conclude at the (a) 0.01, (b) 0.05 level of significance that the variability of class B is greater than that of A (c) What is the P value of the test

Print EAN 128 In NoneUsing Barcode creation for Software Control to generate, create GS1-128 image in Software applications.

Making Code 39 In NoneUsing Barcode creator for Software Control to generate, create Code39 image in Software applications.

(a) We have, on using subscripts 1 and 2 for classes A and B, respectively, s1

RoyalMail4SCC Drawer In NoneUsing Barcode printer for Software Control to generate, create RoyalMail4SCC image in Software applications.

Drawing Bar Code In NoneUsing Barcode encoder for Office Excel Control to generate, create bar code image in Excel applications.

9, s2

GS1-128 Drawer In .NET FrameworkUsing Barcode drawer for Reporting Service Control to generate, create EAN128 image in Reporting Service applications.

Matrix Barcode Generator In C#.NETUsing Barcode maker for .NET Control to generate, create 2D Barcode image in Visual Studio .NET applications.

12 so that 150

Drawing Bar Code In Objective-CUsing Barcode creation for iPhone Control to generate, create bar code image in iPhone applications.

Decode UCC - 12 In JavaUsing Barcode recognizer for Java Control to read, scan read, scan image in Java applications.

n1 n1 1

Drawing Code 39 Extended In Objective-CUsing Barcode drawer for iPad Control to generate, create ANSI/AIM Code 39 image in iPad applications.

Barcode Drawer In JavaUsing Barcode generation for Android Control to generate, create barcode image in Android applications.

s2 1

16 2 (9) 15

86.4,

n2 n2 1

s2 2

25 (12)2 24

We have to decide between the hypotheses H0: s1 H1: s2 s2, and any observed variability is due to chance s1, and the variability of class B is greater than that of A

The decision must therefore be based on a one-tailed test of the F distribution. For the samples in question,

s2 s1

150 86.4

CHAPTER 7 Tests of Hypotheses and Significance

The number of degrees of freedom associated with the numerator is r2 25 1 24; for the denominator, r1 16 1 15. At the 0.01 level for 24, 15 degrees of freedom we have from Appendix F, F0.99 3.29. Then, since F F0.99, we cannot reject H0 at the 0.01 level.

(b) Since F0.95 2.29 for 24, 15 degrees of freedom (see Appendix F), we see that F reject H0 at the 0.05 level either. (c) The P value of the test is P(F software, P 0.134. 1.74). The tables in Appendix F show that P