Chapter 10

Make an assumption about reality, and collect sample evidence to determine whether it contradicts the assumption

denoted Ho is a statement to be tested. A statement of no change, no effect or no difference and is assumed true until evidence indicates otherwise

denoted Ha is a statement that we are trying to find evidence to support

This decision would be correct

This decision would be correct

This decision would be incorrect. This type of error is called a type 1 error

The decision would be incorrect. This type of error is called a Type 2 error

P( type 1 error) = P (rejecting Ho when Ho is true)

P ( type 2 error) = P ( not rejecting Ho when Ha is true)

a is the probability of making a type 1 error the choice of the level of significance depends on the consequences of making a Type 1 error. If the consequences are severe , the level of significance should be small ( say a = .01) . However if the consequences are not severe, a higher level of significance can be chosen (say , a = .05 or a = .1

inverse relation b/t a and B ( one goes up , other goes down)

null hypothesis when the null hypothesis is rejected , we say that there is sufficient evidence to support the statement in the alternative hypothesis. When the null hypothesis is not rejected , we say that there is not sufficient evidence to support the statement in the alternative hypothesis. We never say that the null hypothesis is true

we say that the result is statistically significant and we reject the null hypothesis

is the likelihood or probability that a sample will result in a statistic such as the one obtained if the null hypothesis is true

reject the null hypothesis

Verify the 3 requirements : - the sample is a simple random sample -np (1-p) is greater than or equal to 10 -n is less than .05 N Stat-Proportion Stats - One Sample - With Summary Enter the # of successes and # of observations Choose the hypothesis test radio button . Enter the value of the proportion stated in the null hypothesis and select the correct alternative hypothesis. Click compute

Verify necessary conditions - n po ( 1- po) greater than or equal to 10 - n is less than or equal to .05 N Stat , Proportion Statistics , one sample, with summary enter # of successes and # of trials Choose confidence interval radio button , enter the level of confidence click compute

Hypothesis test for a population proportion : small sample size - stat , calculators , binomial - type values for n and p - select appropriate sign and value of x -click compute

- statistical significance means that the difference between the observed average / proportion and the expected average / proportion is probably not due to chance - it does not imply that the difference has any pratical significance

Verify the 3 requirements - simple random sample - n is greater than or equal to 30 - n is less than or equal to .05 N Stat - T statistics - One Sample - With summary Enter the sample mean, sample standard deviation, and sample size Choose the hypothesis test radio button . Enter the value of the mean stated in the null hypothesis and select the correct alternative hypothesis Click compute

- normal distribution - .05 is less than N -simple random sample Stat - T statistics - One Sample - with data Select column containing the data Choose the hypothesis test radio button. Enter the value of the mean stated in the null hypothesis and select the correct alternative hypothesis Click compute

refers to the idea that, while small differences between the statistic and parameter stated in the null hypothesis are statistically significant, the difference may not be large enough to cause concern or be considered important

the difference b/t the statistic and parameter in the null hypothesis is not enough to be considered practically significant