STATISTICS #3

"Extreme" means:

far from expected if the null hypothesis were true

A Type I error is committed when:

we reject a null hypothesis that is true

T-interval procedure

- The population standard deviation is unknown. - The population is normally distributed. - The sample size is small.

A significance test about a hypothesis has five steps:

1. Hypotheses 2. Significance level 3. Test Statistic 4. Critical Value/ P-value 5. Conclusion

Alternative hypothesis:

A hypothesis to be considered as an alternative to the null hypothesis. We use the symbol Ha to represent the alternative hypothesis.

Null hypothesis:

A hypothesis to be tested. We use the symbol Ho to represent the null hypothesis

Significance test:

A method of using data to summarize the evidence about a hypothesis

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. 23) The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18, the null hypothesis could be rejected at a level of significance of 0.05.

FALSE

True or False: Suppose, in testing a hypothesis about a proportion, the p value is computed to be 22) 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

FALSE

For a "ONE MEAN" hypothesis test use:

If sigma is known or unknown; use either Z-table or T-table

For a "TWO MEAN" hypothesis test use:

Independent or Dependent

Significance level:

The probability of making a Type I error, that is, of rejecting a true null hypothesis.

Hypothesis test:

The problem in a hypothesis test is to decide whether the null hypothesis should be rejected in favor of the alternative hypothesis.

States that the parameter falls in some alternative range of values:

alternative

The value in the alternative hypothesis usually represents

an effect of some type

If a test of hypothesis has a Type I error probability (alpha) of 0.01, we mean:

if the null hypothesis is true, we reject it 1% of the time

The value in the null hypothesis usually represents

no effect

A statement that the parameter takes a particular value:

null

The t test for the mean difference between 2 related populations assumes that the:

population of differences is approximately normal or sample sizes are large enough.

The alternative hypothesis should express what the

researcher hopes to show

Which of the following would be an appropriate null hypothesis?

the population proportion is no less than 0.65 (meaning greater than or equal too)

Define a p-value

the probability of observing a value of the test statistic as extreme or more extreme than the observed (assuming the null hypothesis is true)

If an economist wishes to determine whether there is evidence that average family income in community equals $25,000:

two-tailed test should be utilized

Suppose we wish to test H0: μ ≤ 47 versus H1: μ > 47. What will result if we conclude that the 8) mean is greater than 47 when its true value is really 52?

we have made a correct decision