Chapter 8: Hypothesis Testing

What is the formula for Students t distribution?

(x̅-μ) / (s/√n), s= sample standrad deviation

What is the formula for the standard test statistic Z?

(x̅-μ) / (σ/√n)

To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, how do you decide whether to use the normal or Student's t distribution?

If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n - 1 degrees of freedom.

If we fail to reject (i.e., "accept") the null hypothesis, does this mean that we have proved it to be true beyond all doubt? Explain your answer

No, it suggests that the evidence is not sufficient to merit rejecting the null hypothesis.

If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt? Explain your answer.

No, the test was conducted with a risk of a type I error

CALC VERSION OF FINDING SINGLE PROPORTION Z STAT

STAT - TEST - 1PROPZTEST

CALC VERSION OF FINDING Z STAT

STAT - TESTS - Z TESTS - STATS - ENTER DATA - CALCULATE (DRAW- SHOWS GRAPHS)

When x has a normal distribution with known σ we use what test statistic?

Standrad test statistic- Z

For the same sample data and null hypothesis, how does the P-value for a two-tailed test of μ compare to that for a one-tailed test?

The P-value for a two-tailed test is twice the P-value for a one-tailed test.

In a statistical test, we have a choice of a left-tailed test, a right-tailed test, or a two-tailed test. Is it the null hypothesis or the alternate hypothesis that determines which type of test is used? Explain your answer.

The alternative hypothesis because it specifies the region of interest for the parameter in question.

When you're graphing the statistic and it is a right tailed test which way do you shade?

To the right

H1: μ < 8.3 is a _________ tailed test

left

What does x̅, μ, σ, and n mean?

mean of simple random sample, pop. mean (value stated in null), standard deviation, and sample size

When using the Student's t distribution to test μ, what value do you use for the degrees of freedom?

n - 1

What does P stand for?

population proportion

H1: μ > 8.3 is a _________ tailed test

right

H1: μ ≠8.3 is a _________ tailed test

two

When do you fail to reject the null?

when p value is greater than alpha

When do you reject null?

when p value is less than alpha level

Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg. What would you use for the alternate hypothesis H1?

μ < 60 kg

If you want to set up a statistical test to challenge the claim that μ = 60 kg, what would you use for the null hypothesis H0?

μ = 60 kg

Suppose you want to test the claim that the average weight of such a wild colt is greater than 60 kg. What would you use for the alternate hypothesis?

μ > 60 kg

Suppose you want to test the claim that the average weight of such a wild colt is different from 60 kg. What would you use for the alternate hypothesis?

μ ≠ 60 kg

How do you calc P Value

2nd - distribution - normal cdf - enter range

What are the 5 steps in hypothesis testing?

1) State the null and alternative hypotheses 2) Calculate the test statistic 3) Determine distribution (p value) (assume normal in large numbers when testing hypotheses of means) 4) Choose the level of significance - rejection decision 5) Conclusion

When do we have a risk of Type 2 error?

When we fail to reject null when it was false

When do we have a risk of Type 1 error?

When we reject the null when it was actually true

When is data statistically significant?

When you reject the null

If H0 is rejected at the 1% level will it always be rejected at the 5% level?

Yes

In general, if sample data are such that the null hypothesis is rejected at the α = 1% level of significance based on a two-tailed test, is H0 also rejected at the α = 1% level of significance for a corresponding one-tailed test? Explain your answer.

Yes. If the two-tailed P-value is smaller than α, the one-tailed area is also smaller than α.

When doing a test of a single proportion what is the formula for the statistic Z?

Z= (p̂-p) / (√p x q / n)

What does "α" mean

alpha - level of significance (.01 / .05)