26. Hypothesis Testing

What must be completed before undertaking a test of hypothesis?

Analysis Plan

null hypothesis

States the opposite of what you are trying to prove.

The samples in a test of hypothesis must be _________ selected.

Randomly

Type 1 or Alpha Error

Reached the wrong conclusion

The conventional choice for the Critical P-Value is _______ percent.

0.05 or 5%

3 Hypothesis Tests

1) one sample test 2) two sample test 3) ANOVA

What assumptions must be met before using these tests?

1) that the population from which the samples are drawn must be normally distributed. Confirmation can be informal i..e visual or formal using Chi-Square or Kolmogorov-Smironov (parametric methods). However, assuring the Population be normal is less of a problem as the sample size increases. If distribution is not normal, nonparametric tests must be used.

one sample t test: one and two tailed tests

1) two tailed test is used if deviations of the sample Mean in either direction from the target or population need to be considered. 2) one tailed test is used if deviations in only one direction need to be considered. To determine refer to the null hypothesis. For example, "the population Mean from which the sample was taken is LESS THAN the target of 80". The LESS THAN implies one-tailed test.

A sample of 50 orders is taken from each of 5 distributors. To determine if there is s significant difference in order size across all distributors which test would be run?

ANOVA

What parametric Test is used to determine if there is significant difference between the means of three or more samples?

ANOVA

Calculated p values must be greater than 1.0 to be significant.

False

The objective of a two sample t test is to determine whether three or more sample means come from the same population.

False - determine whether TWO sample means come from the same population.

The most important assumption when using a test of hypothesis is that the sample size must be greater than 50.

False - sample must be normally distributed

At a critical p-level of 0.05 or 5% this implies that there is a 95% chance of committing a Type I error.

False - the probability is only 5% of making a Type I error.

alternate hypothesis

Is always written to express what it is you are trying to prove.

Critical P-Value

Is the probability below which the null hypothesis will be rejected. It expresses the risk we are willing to take in reaching conclusions from the sample. The larger the critical p-value the greater the risk of making a wrong decision when accepting or rejecting the null hypothesis. In most most six Sigma applications the critical p-value is set at 0.05. If the critical P-Value is .05 and the calculated P-Value is 0.02 the null hypothesis would be rejected in favor of the alternative hypothesis. However, if the calculated value is 0.25, the null hypothesis would be accepted.

Calculated P-Value

It represents the probability of observing a sample statistic this far from the target Mean. For example, if the target Mean is 80 while the sample Mean is 82. The calculated p Value would represent the probability of observing a sample Mean (82) this far away from the target Mean (80). The calculator determines the Calculated P-Value.

For a null hypothesis to be rejected the critical p value must be _________ than the calculated p value,

Larger

Hypothesis Testing involves the use of statistics to determine if there is sufficient evidence in a _________ to conclude whether or not a certain condition is true for an entire __________.

Sample, population

A process has been improved. To determine if the new population Mean, is greater than the target how should the null hypothesis be represented?

The new population Mean is not greater than the target.

"There is no difference between sample means" is an ANOVA null Hypothesis.

True

A two-tailed Test is used if deviations of the sample Mean in either direction from the target or population need to be considered.

True

Consider a car rental company that Samples customers to determine their satisfaction with the service. The null hypothesis would state that satisfaction is less than 78 on a scale of 1 to 100. This would require a one-tailed Test.

True

In a one sample t Test the calculated p Value is the probability of observing a sample statistic this far from the target Mean.

True

The critical p-value has the same meaning as the significance level.

True

The purpose of comparing a critical p-value with a calculated p-value is to accept or reject the null hypothesis.

True

The target Mean of a one sample t test is 145. The sample Mean is 140. The calculated p Value would represent the probability of observing a sample Mean this far from the target.

True

To estimate whether or not a distribution is normal, compare a histogram of the sample data with a normal probability curve.

True

ANOVA (ANalysis Of VAriance)

Used to determine if there is significant difference between the means of more than two samples.

Two Sample t Test

Used to determine whether two sample means come from the same population.

Hypothesis Testing

Uses statistics to determine if there is sufficient evidence in a sample to conclude whether a certain condition is true for the entire population.

Analysis Plan

Whenever a hypothesis test is used it is necessary to create an Analysis Plan. Must include: 1) a statement expressing the business or process challenge that will be addressed. 2) a null and alternative hypothesis 3) whether or not the distribution is normal or close to normal 4) sample size 5) one or two sided test 6) significance level, also called Critical Level, for conducting if the null hypothesis can be accepted or rejected