Probability
There is a six sided dice. What is the probability that a 1 is rolled every single time in 3 rolls?
(1/6)(1/6)(1/6)=1/216 or .462%
What type of test are you supposed to run for means?
What is a t-test.
How does a control group benefit an experiment?
it provides a baseline for comparison to see if the treatment has an effect. Without it, it hard to observe whether changes are due to treatment or other factors.
What is a Type II Error in testing?
When you fail to reject the null hypothesis (Ho) but the alternative or (Ha) is actually true.
A random 95% confidence interval for a population mean in (15.3,19.8). If you wanted a 99% confidence interval instead, how would the interval change? Wider or Narrower?
The Interval would get wider.
In a bag there are 10 blue shirts, 12 orange shirts, 8 red shirts, and 9 white shirts. If one shirt is selected from the bag at random, what is the probability that it is a Blue Shirts OR and Orange Shirt?
(10/39)+(12/39)=(22/39) or .5641
When is it appropriate to use the 10% condition and when is it appropriate to not?
Use it when you are sampling without replacement and do not use it when you are sampling with replacement.
What is confounding variable, and why is it a problem in experiments?
This variable is an outside factor that affects the response and is related to the explanatory variable. It can make it difficult to determine whether changes in response variable are due to the treatment or the confounding variable.
When should a t-distribution be used instead of a Z-distribution?
A t- distribution should be used when testing means and a Z-distribution should be used when estimating proportions.
A six sided dice is rolled once. What is the probability of rolling a number greater than 4?
(2/6)=0.33333
Given that events A and B are independent, P(A)=0.4 and P(B)=0.3, what is the probability of P(A or B)
P(A or B)= 0.4+ 0.3-0.12=0.58
In a chi square test for goodness of fit, all expected counts must be this value.
All expected counts need to be greater than or equal to 5.
Why is replication important in experiments?
Replication is important in experiments because ot ensures results are not from chance and that increases the reliability and generalization of the experiment.
What is the correct interpretation of a confidence interval at a 95% confidence mean?
We are 95% confident that the interval of (blank) to (blank) captures the true population mean. (in context)
A 90% confidence interval means that 90% of the data value lies with the calculated interval? True or False?
False, because a confidence interval estimates the range for a parameter, this does not include individual data values
The random variable X can be either 0,1,2,3,4 or 5. The expected value of X is 4.1. Interpret the expected value of the variable X.
If you observe many, many values of X, the average of those values would approach 4.1
A student is conducting a two-sample t test to compare the average sleep time of students at different schools. There is one random sample of 12 students and another random sample of 18 students. The distributions of both the sleep times are slightly skewed. Why should they proceed with caution?
Because the approximately normal condition is not met because both of the sample sizes are below 30. There is also slight skew.
What is the difference between an observational study and an experiment?
Observational study is when researchers observe outcomes and results without assigning treatments. Experiments however assign treatments to observe their effects.
How does increasing the sample size affect a confidence interval?
A Larger sample size decrease standard error which allows the confidence interval to be narrower
A smaller sample size increases standard error which allows the confidence interval to be wider.
When do you use pooling in stats?
You use pooling only in a Two-proportion Z test, two sample proportions
The probability of the hitter getting a hit is 0.301. What is the probability that the hitter gets his first hit on the 4th at bat or later?
1-geometcdf(P=.301, X=3)=.3416
You are running a linear regression T-Test with a random sample of 12 students. Assuming all the conditions are met, describe all the conditions besides the linear one.
Independence:
Random: Random sample of 12 students
10%: Sample of 12 students is less than 10% of the population of ALL students.
Approx Normal: Dotplot of the residuals shows NO strong skew NOR outliers.
Equal SD: Residual plot shows similar scatter around "Residual= 0" for each x value.
What is the purpose of random assignment in an experiment?
Purpose is to reduce bias and ensure that treatment groups are as similar as possible. Helps establish cause and effect
At what significance levels would you reject Ho from a one sided test with an observed computer output p value of 0.15? Significance level of 0.05 or 0.10?
you could reject at 0.1 level because computer output gives you a double sided p value. Therefore if you divide it by 2 for a one sided test, you can reject Ho at the 0.1 significance level.
In an experiment of 100 high school students, we found that 70 of them play a sport. A 95% confidence interval for the true proportion of high school students who play sports is calculated to be approximately (0.62-0.73). Interpret AND explain the interval in context.
Interpretation: We are 95% confident that the interval 0.62-0.73 captures that the true population proportion of all high school students who play sports.
Meaning: If we were to take many, many samples of 100 high school students and build a confidence interval for each one, about 95% of those intervals would contain the true population proportion of all high school students who play sports.