Vocabulary
What is the p-level that determines if we reject or fail to reject the null hypothesis?
Alpha Level (Significance Level)
What are the null and alternative hypotheses for a 1-prop Z-test?
H0: p = #, HA: p >,<, ≠ #
What are the null and alternative hypotheses for a 2-prop Z-test?
Ho: p-hat1 = p-hat2 , HA: p-hat1 >,<, ≠ p-hat2
What is the assumption that makes sure the sample is representative?
Random Assumption
A truck company wants on-time delivery 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R Us) unless there is evidence that this new manufacturer cannot meet the 98% pn-time goal. As a test, the truck company purchases a random sample of metal parts from Steel-R Us, and then determines if these parts were delivered on time. Which hypothesis should they test?
HO: p = 0.98 , HA : p < 0.98
What is the ability of a test to correctly reject the null hypothesis?
Test Power
What is the equation for calculating the Z Value of a 1-prop Z-test?
z = (p-hat( 1 - p-hat)/n)½
How do you calculate the pooled statistic of a 2-prop z- test?
p-hat = (x1 + x2)/ (n1 + n2)
What is the assumption that is determined by the s/f condition?
Sample size assumption
A confidence interval for a proportion is 0.251 to 0.335. What are the point estimate and the margin of error for this interval?
0.293,0.042
What is the term for how much different random samples vary from one another within a population?
Sampling Variability
What is the equation for calculating the interval of a 1-prop Z-interval?
p-hat ± z* (p-hat( 1 - p-hat)/n)½
What is the equation for calculating the standard deviation of a 2-prop Z-test?
SD: (p-hat( 1 - p-hat) (1/n1 + 1/n2))½
How are the assumptions and conditions different between a 1-prop confidence interval and a 1-prop hypothesis test?
There is no difference
Suppose that a conveyors used to sort packages by size does not work properly. We test the conveyor on several packages (with: HO: incorrect sort) and our data results in a P-value of 0.016. What is the conclusion of our testing based on this data at an alpha level of 0.05?
We reject HO, making a type I error
What occurs when a test incorrectly rejects the null hypothesis even though it is actually true?
Type I Error
What is the formula for the parameter of a 1-prop Z-test/interval?
N(p, SD)
What is the equation for calculating the interval of a 2-prop Z-interval?
(p-hat1 - p-hat2) ± Z* (SE)
Samantha wants to find out if the proportion of people that own at least one pet at her large school matches the national average of 39 percent. She takes a random sample of 48 people from her school and finds that 21 people own at least one pet. Are all assumptions and conditions satisfied and why or why not?
The random assumption is satisfied because the sample is stated to be random. The independence assumption is satisfied because the sample size is less than 10% of the school population. The sample size assumption is satisfied because there are 21 successes and 27 failures each is more than 10.
We have calculated a confidence interval based on a sample of n = 200. Now we want to get a better estimate with a margin of error only one-fifth as large. What should the sample size be?
At least 5000
What is the statistical principle that proposes that if you take a sufficiently large sample, the sample distribution will be approximately normal?
Central Limit Theorem
Maryland’s Motor Vehicle Administration (MVA) claims that 60% of all teens pass their online driving test on the first attempt. An investigative reporter examines an SRS of the MVA records for 175 teens in MD. 96 of them passed the test on their first try. What are the parameters of this 1-prop z-test?
N(.60, 0.0370)
A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 400 people shows that 28% of those 200 who were contacted by telephone actually made contributions compared to only 18% of the 200 who receive first class mail requests. Which formula calculates the 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail?
(0.28 - 0.18) ± 1.96 ( (((.28)(.72))/200) + (((.18)(.82))/200))½
A healthcare company wants to test the effectiveness of a new blood pressure medication. They use a group of 100 participants who each choose to take the medication or a placebo, and measure their blood pressure before and after the treatment to determine whether blood pressure decreased with the medication. They found that 18 of the 50 who took the placebo had their blood pressure decrease significantly, and 31 of the 50 who took the medication had their blood pressure decrease significantly. Are all assumptions and conditions satisfied and why or why not
The random assumption is not satisfied because participants choose their treatment, so proceed with caution. The independence assumption is satisfied because 100 is less than 10% of the total amount of people with blood pressure issues, the independent groups' assumption is satisfied because people are only assigned to one or the other. The sample size assumption is satisfied because there are over 10 successes and failures.
We are about to test a hypothesis using data from a well-designed study. Which is true?
A small P-value would be strong evidence against the null hypothesis
We can set a higher standard of proof by choosing alpha = 10% instead of 5%
If we reduce the alpha level, we reduce the power of the test
I and III only