MATH 240. Chapter 8 Outlines of Hypothesis Tests

Size: px

Start display at page:

Download "MATH 240. Chapter 8 Outlines of Hypothesis Tests"

Lucinda Rice
5 years ago
Views:

1 MATH 4 Chapter 8 Outlines of Hypothesis Tests Test for Population Proportion p Specify the null and alternative hypotheses, ie, choose one of the three, where p is some specified number: () H : p H : p (Two-tailed test) () H : p H : p (Right-tailed test) (3) H : p H : p (Left-tailed test) Select the significance level 3 Compute the test statistic from sample data z pˆ p p q / n where q p () reject H if the value of z is in the two-tailed critical region, ie, when z z / or when z z / () reject H if the value of z is in the right-tailed critical region, ie, when z z (3) reject H if the value of z is in the left-tailed critical region, ie, when z z The sample is a simple random sample The conditions np 5and nq 5 are both satisfied, so that the test statistic can be approximated by a normal distribution

2 Test for Population Mean ( known) Specify the null and alternative hypotheses, ie, choose one of the three, where is some specified number: () : () : (3) : H : H : H : H (Two-tailed test) H (Right-tailed test) H (Left-tailed test) Select the significance level 3 Compute the test statistic from sample data x z n () reject H if the value of z is in the two-tailed critical region, ie, when z z / or when z z / () reject H if the value of z is in the right-tailed critical region, ie, when z z (3) reject H if the value of z is in the left-tailed critical region, ie, when z z The sample is a simple random sample The population standard deviation is known The sample size n is large (n > 3) or the population is normally distributed

3 Test for Population Mean ( not known) Specify the null and alternative hypotheses, ie, choose one of the three, where is some specified number: () : () : (3) : H : H : H : H (Two-tailed test) H (Right-tailed test) H (Left-tailed test) Select the significance level 3 Compute the test statistic from sample data x t s n () reject H if the value of t is in the two-tailed critical region, ie, when t t / or when t t /, where df = n () reject H if the value of t is in the right-tailed critical region, ie, when t t, where df = n (3) reject H if the value of t is in the left-tailed critical region, ie, when t t, where df = n The sample is a simple random sample The population standard deviation is not known The sample size n is large (n > 3) or the population is normally distributed 3

4 Chapter 9 Outlines of Hypothesis Tests Test for the difference between two population proportions p p Specify the null and alternative hypotheses H : p p H : () p p (Two-tailed test) () p p (Right-tailed test) (3) p p (Left-tailed test) Select the significance level 3 Compute the test statistic from the sample data z pˆ pˆ pq n n x x where p and q p n n () reject H if the value of z is in the two-tailed critical region, ie, when z z / or when z z / () reject H if the value of z is in the right-tailed critical region, ie, when z z (3) reject H if the value of z is in the left-tailed critical region, ie, when z z 5 Conclusion, ie, state the previous decision in nontechnical terms The two samples are both simple random samples and independent The conditions npˆ 5 and n qˆ 5 are satisfied for each of the two samples 4

5 Test for the difference between two population means (independent samples) Specify the null and alternative hypotheses H : H :() (Two-tailed test) () (Right-tailed test) (3) (Left-tailed test) Select the significance level 3 Compute the test statistic from the sample data t x x s n s n () reject H if the value of t is in the two-tailed critical region, ie, when t t / or when t t /, where df = smaller of n and n () reject H if the value of t is in the right-tailed critical region, ie, when t t, where df = smaller of n and n (3) reject H if the value of t is in the left-tailed critical region, ie, when df = smaller of n and n t t, where The two samples are both simple random samples and independent The two samples are both large (ie, n 3 and n 3 ) or both samples are taken from populations with normal distributions 5

Procedure for Finding P-Values Figure 8-6 Copyright 7

6 Wording of Final Conclusion Figure 8-7 Copyright 7 Pearson Education, Inc Publishing as Pearson Addison-Wesley Slide 48 Procedure for Finding P-Values Figure 8-6 Copyright 7 Pearson Education, Inc Publishing as Pearson Addison-Wesley Slide 44 6

Chapter 8. Inferences Based on a Two Samples Confidence Intervals and Tests of Hypothesis

Chapter 8. Inferences Based on a Two Samples Confidence Intervals and Tests of Hypothesis Chapter 8 Inferences Based on a Two Samples Confidence Intervals and Tests of Hypothesis Copyright 2018, 2014, and 2011 Pearson Education, Inc. Slide - 1 Content 1. Identifying the Target Parameter 2.