P-values and Significance

Null Hypothesis (H₀)

The null belief about a parameters’ value, often called the “dull” hypothesis - nothing new or interesting happening. Assumed to be true, until evidence convince us otherwise.

Alternative Hypothesis (H_A)

Our unproven belief about a parameter’s value, for which we have to father evidence. Often called the “research” hypothesis - it’s what our studies aim to demonstrate. Not assumed to be true: we have to collect evidence to support it.

(p-value < a) → we reject H_{0 → ____} H_A

Convincing evidence

(p-value > a) → we fail reject H_{0 → ____} H_A

Don’t have convincing evidence

H₀

What is believed/assumed to be true

H_A

Not assumed to be true … need evidence (low p%)

Conclusion

Because (p-value) >/< (significance level), we fail to reject/reject H₀ and we do/do not have convincing evidence that (H_A in context).

Is this convincing evidence?

Because (p-value) >/< (significance level), we fail to reject/reject H₀ and we do/do not have convincing evidence that (H_A in context).

Does she have convincing evidence that the school is incorrect/

Assuming H₀ is true (p-level) there is a 0.166 possibility a o hate of (blank) or greater is purely by chance. Because (p-value) >/< (significance level), we fail to reject/reject H₀ and we do/do not have convincing evidence that (H_A in context).

A one sample z-test for a population proportion will be conducted using a simple random sample selected without replacement from a population.

The population size is more than 10 times the sample size.

Consider a population with population proportion p. and a sample from the population with sample proportion p. Which of the following describes the purpose of the one-sample a test?

To estimate the probability of observing a value as extreme as p hat given p

For a one-sample test for a population proportion p and sample size n, why is it necessary that no and n (1 - Po) are both at least 10

The sample size must be large enough to support an assumption that the sampling distribution of the sample proportion is approximately normal.

the results of a hypothesis test, which indicate there is not enough evidence to reject the null hypothesis. Which of the following statements about error is correct?

Type Il error could have been made, but not a Type I error.

which of the following should the researchers do to avoid the more consequential error?

Increase the significance level to increase the probability of a Type I error.

The following list shows three factors that can either increase or decrease the probability of a Type II error.

I The sample size is increased

11. The significance level is increased

Ill. The standard error is increased

Which factors alone will cause the probability of a Type Il error to increase?

III

Which of the following is the best interpretation of the power of a significance test?

Power is the probability of detecting an effect if an effect exists.

Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces.

The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces.

Apropiarte test for analysis

A two-sample e-test for a difference in population proportions

Great Power (Increases Type Error 2)

-Sample Size Increase

-The Significance level (a) increases

-Standard error decreases

-True parameter value is further

Past studies indicate that roughly 20% of adults get less than 5 hours of sleep each night. A sor

p-valae

scientist believes the percentage is less for adults in a particular age group. The social scientist

probat libtained a random sample of adults in this age group and conducted a test of Ho : P = 0.20 versus

M, : P ≤ 0.20. The p-value of the test was 0.064, Which of the following is a correct interpretation of the p -value?

20% of adults in this age group get less than 5 hours of sleep each night, the probability of obtaining a sample proportion as small or smaller than the one obtained by the social scientist is 0.064.

Regular wellness check-ups with a family doctor are seen as helpful for the early detection of medical conditions. A random sample of adults is chosen to test the claim that less than 25 percent of adults see their family doctor for regular wellness check-ups at a significance level of 0.05. The test yielded a p -value of 0.03. Assuming all conditions for inference were met, which of the following is the correct conclusion?

We do not reject the null hypothesis

E/We reject the null hypothesis. There is convincing evidence that less than 25 percent of adults see their family doctor for regular wellness check-ups.

(310

0.03 < 0.05

Which of the following is the best explanation for why random assignment is necessary wher performing a significance test based on data from an experiment?

So the results from the sample can be generalized to a larger population

Differ

≠

Z score for two sample

(p̂1-p2)-0/p̂(1-p̂)(1/n1+1/n2)

H0 for 2 sample

H0: p1=p2, H0: p1-p2=0

HA for 2 samples

HA: p1>p2, HA: p1-p2>0