Confidence Intervals
What is the general formula to create ANY confidence interval?
Point Estimate +/- Critical Value * Standard Deviation/Error
What is the general formula for a standardized test statistic?
(statistic - parameter) / Standard Deviation/Error
A False Positive is what type of statistical error?
Type I Error
How many conditions are there to usually check?
3
What is type I error?
When you reject the null hypothesis in the case that you should have failed to reject.
Interpret a 95% confidence interval of (1.02, 3.45) for mean amount of siblings a student has at Rice.
We are 95% confident that the true mean amount of siblings someone has at Rice is captured by the interval of (1.02, 3.45).
What must you do with the p-value if you are conducting a two-sided test by hand (alternative hypotheses is "not equal")
multiply the p-value you get by 2
What is the probability of a type I error occurring equal to, usually?
alpha = 0.05
What are the conditions for a One Sample t-interval or t-test?
Random sample must be taken, sampling distribution of X̅ must follow the central limit theorem or distribution must be stated as approx. normal, and the sample must be less than 10% of the population.
What test should be used if the 2 samples are NOT independent from one another (think of Unit 3)
Paired t-test for mean difference
Same as matched pairs t-test for mean difference
What is the t-critical value for a 96% confidence interval for a quantitative sample whose sample size is 5?
2.999
The equation for finding the standard deviation for 2 sample mean is...
sqrt [(s1^2/n1) + (s2^2/n2)]
The probability of a type II error is denoted by what greek letter?
Beta
(DD!) With sample size 20 and population size 50, is the condition for independence satisfied? Why or why not?
No, does not pass 10% Condition.
How old is Hazel, Mocha, & Austin (300 points for each correct answer)
Hazel = 2 years old
Mocha = 9 months old
Austin = 10 months old
What is the margin of error for a 95% confidence interval for proportions with a sample proportion of 0.56 and a sample size of 439?
What is 0.046?
What is the p-value for a 1 proportion z test if your true mean is 0.5, the sample mean is .45, and your sample size is 100 (conduct one-sided test)
0.1587
1) Decrease beta P(Type II Error)
2) Increase sample size
3) Increase alpha P(Type I Error)
If a "means" problem has a sample size smaller than 30, how can the normal condition still be met?
1) if prompt says pop distribution is normal
2) if raw data histogram/dot plot shows no outliers or skew
45 out of 100 students from Rice drive to school. 57 out of 102 SBHS students drive to school. Find the pooled p proportion. (p-hat c)
0.505
Is there convincing evidence that more Rice Students go to sports games than Burlington students? The confidence interval for the difference in proportions was found to be (-0.12, 0.25). Why or why not?
No there is not, the interval contains zero.
What is your conclusion if the test statistic of a 2 sample t-interval if t=2.045 (sample size is 18)
probability of observing the sample difference xbar1-xbar2 or higher is 0.028 purely by chance. Since 0.028 < 0.05, we reject ho and have convincing evidence that alternative hypothesis may be true.
Which is worse for the dogs, a type I or type II error:
Ho: The invisible dog fence does not work
Ha: The invisible dog fence does work
Type I error, believing the fence works when in reality it doesn't the dogs can escape and get injured.
Which tests and intervals should the conditions be checked for individual groups?
2 sample t-test for u1-u2
2 sample t-interval for u1-u2
2 sample z-test for p1-p2
2 sample z-interval for p1-p2
In a recent census, it was found that the population proportion of babies born male was 0.5. Researchers took a random sample of 200 babies and found that 96 were male. Is the proportion of babies born male different from 0.5?
Assuming Ho is true, there is a 0.56 probability of observing a stat of .48 or lower, or .52 or higher purely by chance. Since 0.56 > 0.05. We must fail to reject the null hypothesis; there is insufficient evidence to support the claim that the proportion of babies born male is different from 0.5.