General Inference Knowledge
The two types of inference.
Confidence intervals and significance tests
The procedure you use to estimate a population proportion by creating a range of values that center around a sample proportion.
one sample z interval for p
The point estimate for a confidence interval for a difference of proportions
p^1 - p^2
What is the formula for the standard error in a hypothesis test for one proportion?
Standard Error = √[(po * (1 - po))/n
If the P-value is less than the significance level (α), do we reject or fail to reject the null hypothesis?
We reject the null hypothesis.
The general formula for margin of error.
critical value * standard error
DOUBLE JEOPARDY!!
True or False: A larger sample size leads to a smaller margin of error in a confidence interval.
True.
The procedure you use to estimate a difference in population proportions by creating a range of values that center around the difference of two sample proportions.
two sample z interval for p1 - p2
The name for the probability of observing a sample result as extreme as, or more extreme than, the one obtained if the null hypothesis is true?
P-value.
The procedure you use to determine if there is convincing evidence to support a hypothesis about a difference in population proportions.
two sample z test for p1 - p2
The three conditions that must be checked before creating a confidence interval or performing a significance test.
random sampling, 10% condition, and large counts
The 95% confidence interval to estimate the proportion of all residents of the town who support a political candidate is (0.36,0.57). Interpret the interval.
We are 95% confident that the interval (0.36, 0.57) captures the true proportion of residents of the town who support the political candidate.
Two populations are both size 500. The sample proportions collected from each are 12/45 and 17/60. Which condition will not be passed?
10% condition
A representative for a large factory believes that more than half the workers at the factory want the opportunity to work more overtime hours. State a hypothesis you could use to test this belief.
Ho: p = 0.5
Ha: p > 0.5
Your two sample proportions are 43/67 and 32/55. Find pc , the combined/pooled proportion.
75/122
The reason we check the large counts condition.
So that we can assume that the sampling distribution is approximately normal.
True or False: 92 out of 100 residents in a random sample are in favor of a new proposal. It is appropriate to assume that the sampling distribution of the sample proportion is approximately normal.
False
If the confidence interval for the difference in proportions includes zero, what does it suggest about the two proportions?
It suggests that there is no statistically significant difference between the proportions of the two groups.
How is the significance level (α) related to the probability of making a Type I error in hypothesis testing?
The significance level is the probability of making a Type I error.
The power of a hypothesis test in which the significance level is 0.05 and the probability of a Type II error is 0.18.
0.82
The reason we check the 10% condition.
So that we can sample without replacement/ use the standard error formulas.
A 90% confidence interval for the proportion of all people in the country who are worried about inflation is (0.66,0.84). State a claim that is supported by this interval.
More than half/more than 60%/more than 65% of people in the country are worried about inflation.
DOUBLE JEOPARDY!!
The critical value for a confidence level of 92%.
1.75
What is a Type II error in hypothesis testing for proportions?
A Type II error occurs when the alternative hypothesis is true, but you failed to reject the null hypothesis.
Researchers conducted an experiment in which people with a certain condition were given either a drug or a placebo. At the end of the experiment, they will measure the proportion with improved symptoms. They suspect that the drug will be more effective than the placebo. What is an appropriate hypothesis?
Ho: pd = pp
Ha: pd > pp