Ch. 20

basic idea of significance

if you want to prove a claim false then find evidence that is impossible to occur if the claim is true (reject Ho so that accept Ha)
-if your claim is true then this piece of evidence should not have occurred, but since it did that means your claim is fal

there are four basic parts to a hypothesis test:

1. set up your hypotheses (claims test about p)
-the null hypothesis (Ho, the one we try to prove false)
-the alternative hypothesis (Ha, the one we try to accept)
-try to suggest Ha is true once we prove Ho is false
-P is the true proportion and Po is cl

the null hypothesis

-based off no changes in proportions from population to sample.
-Ho: parameter=hypothesized value
-the one we try to prove false
-significance test is testing claim of the null hypothesis
-looking for evidence that goes against Ho
-set up null hypothesis

the alternative hypothesis

-Ha contains the values of the parameter we consider plausible when we reject the null
-we look for evidence that supports Ha
-the hypothesis we accept once we reject Ho
-when they state the problem, they are stating it in terms of the alternative hypothe

one-proportion z-test

the conditions for the one-proportion z-test are the same as for the one-proportion z-interval
-we test the hypothesis Ho: P=Po using the statistic z= (p hat - Po)/SD(p hat)
-we use the hypothesized proportion to find the standard deviation, SD(p hat)= sq

test statistic

-after you state your hypotheses, then you want to find the test statistic which is p
-p value is the likelihood your evidence of Ho is true
-the ultimate goal of the calculation is to obtain a P-value
-the p-value is the probability that the observed sta

A 1996 report from the US consumer project safety commission claimed that at least 90% of all American homes have at least one smoke detector. A city's fire department has been running a public safety campaign about smoke detectors consisting of posters,

1) Ho: p=0.9 (if concerted efforts had no effect, then the proportion of people who have smoke detectors is 90%)
Ha: p > 0.9 (show proportion of people who have smoke detectors is greater than 90%)
-trying to suggest that effort has raised the national ra

According to Mars, there are supposed to be 20% orange M&Ms in the bag. The bag of 122 that you just opened had only 21 orange ones. Does this contradict the company's 20% claim?

p=% of orange candies
1) Ho: p=0.2
Ha: p does not equal 0.2 (asking to suggest that the proportion of orange candies is different from the Po (two sided alternative bc could be greater than or less than))
2) p hat =21/122= 0.07 (supports Ha and goes again

levels of significance

?=alpha
-level that you are going to set as unusual (like if ?=0.05 then p<5% is unusual or if ?=0.1 then p<10% is unusual)
?=0.05
-the evidence will occur in 5 out of 100 samples
-if ? not stated in problem, then assume that level of significance is 5%
?

calculator

Test -> z -> 1-p and then enter in the set up

A large city's department of motor vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter's survey of 90 randomly selected local teens who had taken the test found only 61 who passed.
Does this finding suggest that the passin

p=% of people who passed the test
1) Ho: p=0.8
Ha: p < 0.8 (trying to show proportion of people who passed the test is less than 80%)
2) p hat= 61/90=0.678 (supports Ha and against Ho)
3) make a model centered at 0.8
-st dev: square root ((0.8 x 0.2)/90)

using critical values (Z*) to determine significance

If |Z| > Z* then you have significance
-this eliminates you having to get a p value
-can instead compare z value to critical value to see if significant
1) one sided alternative at ?=0.05
-either right or left tail can be 5% which means that middle is 90%

Anyone who plays or watches sports has heard of the "home field advantage." Teams tend to win more often when they play at home. or do they? if there were no home field advantage, the home teams would win about half of all games played. In the 2007 Major

1) Ho: p=0.5 (don't think is true bc evidence goes against it)
Ha: p>0.5 (evidence supports it)
evidence=54.26%
3) Find critical value
-if using ?=0.01 then that means both tails can be 1% and in the middle is 98%
-use invnorm(0.99, 1, 0) to find Z*=2.33

use confidence intervals to determine significance

-only works when we have a two sided alternative because if have significance at ?=0.05 then both tails add up to 5% (so one tail is under 5% so if significant for two sided alternative then significant for one sided alternative since both are less than 5

Advances in medical care such as prenatal ultrasound examination now make it possible to determine a child's sex early in a pregnancy. There is a fear that in some culture some parents may use this technology to select the sex of their children. A study f

Ho: p=0.517
Ha: p doesn't equal 0.517
p hat= 0.569
1) use 95% CI because they didn't specify
use 1 prop z int (x: 313, n: 550, c: 0.95) to find CI of (0.527, 0.61)
2) evidence suggests proportion of male birth have changed because 51.7% falls outside of t