Conditions
Intervals
Tests
Types of Errors
100
What are the three conditions that must be met for inference testing?
Random
Large Counts
10% Rule
100
What are the steps in the calculator to find the 2 sample t- interval?
Menu -> Statistics -> Confidence Intervals
100
What does "t" stand for in significance tests?
What is, it stands for the test statistic.
100
How many types of errors are there?
What is 2
200
What is the large count condition
The sample size must be 30 or the sample must be symmetric without outliers.
200
When asked to construct an interval, what must you include in your answer (3C's)
Condition Check
Calculator input
Conclusions
200
What is the general formula for a test statistic?
(statistic - parameter)
------------------------
standard deviation of statistic
200
What are the errors called?
What is type one and type two
300
What is the 10% rule and when do we need to check it?
Sample size < 10% of the Population size
Or 10(sample size) < the population size
When sampling without replacement. (When the population size is given.
300
If there is a condition missing in the plan step, what needs to be done?
What is, address it in the conclude step
300
What is the formula for the test statistic for a 1 sample t test?
(x_bar - Mu)/(s/sqrt(n)
300
What is the format for these errors?
Type one: Finding convincing evidence that ____ , when there wasn't.
Type two: Not finding convincing evidence that _____, when there was.
400
Students in an AP Statistics class wants to estimate the proportion of pennies in circulation that are more than 10 years old. To do this, they gathered all the pennies they had in their pockets and purses. Overall, 57 of the 102 pennies they have are more than 10 years old.
Determine if all of the conditions are met.
What is we can assume the it's random because the students randomly received pennies.
What is it is safe to assume that there are more than 1,020 pennies in circulation in the US
102 is greater than 30
400
What is the formula for a one sample interval
x_bar + or - t (s/sqrt(n))
400
Using the formula only, what is the test statistic
mu =20
x-bar = 30
Sx = 2.5
n = 30
What is
t = 21.909
400
A study is trying tell if there is a difference in the language skills and mental development of two groups of 24-month-old children. One group consisted of children identified as talkative, and the other group consisted of children identified as quiet. The scores for the two groups on a test that measured language skills are shown in the table below.
If the studied claimed that there was not enough evidence to claim a cognitive difference between the groups, but one did exist, what type of error would this be?
Type II
500
Construction zones: to see if drivers obey lower speed limits, a police officer used a radar gun to measure the speed (mph) of a random sample of 10 in a 25 mph construction zone. Here are the results:
27 33 32 21 30 30 29 25 27 34
Sample mean - 28.8
Sample Standard Dev - 3.93
Is there convincing evidence that the avg. speed of drivers in this zone is greater than the posted 25 mph speed limit?
Conditions:
Random - They used a random sample
Lage Counts - The sample is symmetric with no outliers (Draw diagram)
Calculator
t-interval( x_bar=28.8, s=3.93, n=10)
(25.9, 31.6)
Conclusion: Since 25 is less than our lower bound
500
A sociologist will conduct a two-sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor’s degrees and people with master’s degrees. From a random sample of 32 people with a bachelor’s degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 30 people with a master’s degree, the average salary was $58,000 with a standard deviation of $4,000.
Is this enough statistical evidence to claim people with master's degrees make more money than people with bachelor's degrees?
Conditions
Random - They used random samples
Large Count - Both sample sizes are over 30
Calculator
2 sample t-test(55000, 3500, 32, 58000, 4000, 30, <) -> p-value=0.001
Conclusion
Since the p-value of 0.001 is less than 0.05, we will reject the null hypothesis. This means there is enough evidence to claim that people with master's degrees make more than people with bachelor's degrees.
500
A manufacturer claims its Brand A battery lasts longer than its competitor’s Brand B battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table below.
What would the Type I error be in this context?
The test concludes that there is enough evidence to claim Brand A batteries last longer, when really Brand B batteries last longer.