Confidence Intervals
The 95% confidence interval for the proportion of people with blue eyes is (0.05, 0.11). How would you interpret this?
We are 95% confidence that the true proportion of people with blue eyes is between 5% and 11%.
What is the 10% rule?
If you are sampling without replacement, your sample size has to less than 10% of your population size.
That is n<0.10N
What does p stand for?
Population Proportion
Rejecting the Null Hypothesis, when it is true.
What is Type 1 error?
If the p-value is less than the significance level, then we, ...
Reject the null Hypothesis.
The 90% confidence interval for the proportion of Austin residence who have been to the zoo in the last year is (0.11, 0.15). The city is thinking of increase the zoo's budget, but only if more than 13% of people go to the zoo each year. According to this interval should the city increase the zoo's budget? Why or why not?
No, the 90% confidence interval contains values greater than and less than 13%. Therefore, we do not know if more than 13% of people went to the zoo without doing a follow up study.
What are the steps to get to the 1 proportion Z-test on your calculator?
Menu -> Statistics -> Stats Tests -> 1Prop_Ztest
What are the three types of alternative hypothesis?
HA:p > p0
HA : p < p0
HA: p is not equal to p0
Type II error.
What is the failing to reject the null hypothesis when, the null hypothesis is false?
If we fail to reject the null hypothesis what do we conclude?
There is not enough evidence.
How would you interpret a confidence level of 90%?
In repeated samples, the confidence interval created from the sample will capture the true population proportion 90% of the time.
What are the three conditions for inference testing?
The sample must be randomly taken
n<10%N, If sampling without replacement
10 success and 10 failures
You are testing two flu drugs A and B. Drug A works on 41 people out of a sample of 195. Drug B works on 351 people in a sample of 605. Are the two drugs comparable? What are your hypothesis?
H0: pA=pB
HA:pA is not equal to pB
The Power of the Test.
What is the probability that the test will correctly reject the null hypothesis?
When do we claim there is enough evidence to support the alternative hypothesis?
If the p-value < significance level
73 people out of a sample of 100 have black hair. What is the 95% confidence interval for the population proportion of people with black hair?
(0.643, 0.817)
51 out of 60 students sample picked statistics as their favorite class. Mr.Hooper uses this sample to do an inference test to determine if over 75% of his students would pick stats as their favorite class. What error did Mr.Hooper make?
Only 9 students selected other classes which is less than 10, and 10 is the required number of failures according to the CLT.
A soda company is concerned that people think their drinks are too sugary. They want to see if the majority of their customers think their drinks are too sugary. Define p and tell what null and alternative hypothesis should they use?
p = proportion of all customers who think their drinks are too sugary
H0: p=0.50
HA:p>0.50
A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require cars to be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop’s license if they find significant evidence that the shop is certifying vehicles that do not meet standards.
What type of error would the shop owners likely find more serious?
Type I error
When can you claim that there is enough evidence to support the null hypothesis?
Never
Texas - Oregon
(0.284, 0.392)
A recent survey of students showed that 107 out of 200 the students surveyed owned a pet. The student council wanted to test if at least 50% of students had a pet. What is the formula for the correct test statistic?
(107/200-0.50)/sqrt((0.5)(0.5)/200)
Market researchers interviewed a random sample of 60 men and a random sample of 55 women about their preferences for different color designs for the packaging of a certain product. The market researchers wanted to see if there was a difference in preference between men and women.
What should their null and alternative hypothesis be?
H0: pm=pf
HA:pm not equal to pf
The 4 things that increase the power of a test.
Increasing Sample Size
Increasing Significance Level
Standard Error Decreases
The true population proportion is further from the null proportion.
You are trying to determine if a coin is fair (50/50 flip). You flip the coin 100 times and get 62 heads. Perform a hypothesis test with a significance level of 5% and state your conclusion.
We get a p-value of 0.0164 which is less than 0.05. Therefore, we have enough evidence to reject the null hypothesis and support the claim that the coin is not fair.