Random variable/binomial random variable
Define X as the number of tires a truck driver gets replaced in a year. Is this a discrete random variable, continuous random variable, or not a random variable?
Discrete random variable
You ask 80 people whether chocolate glazed is their favorite donut or not; 20 say yes. State whether the quantity we can calculate from the given information is a statistic or parameter. Calculate and express the value being sought using the correct notation.
Statistic. P-hat = 20/80 = 0.25
True or false: "A hypothesis test establishes the truth of one of the two hypotheses, either the null or the alternative one.''
False.
We could always make a type I or type II error.
Also, if we fail to reject, we do not endorse either hypothesis as correct.
A bag is full of marbles: 10 red, 10 blue, and 10 green. You draw five marbles (without putting them back) and count how many reds you get. Does the number of reds you get represent a binomial random variable? If so, what are n and p? If not, say why not.
No, the probability of success p is changing each time! In other words, each draw is not independent of the previous one.
The population distribution is the distribution of cases in the population. A sample distribution is the distribution of cases in the sample. The sampling distribution is the distribution of _______?
sample statistics (e.g. sample means or sample proportions)
You run a hypothesis test to see if the mean height of Wellesley students is different from 64 inches. You fail to reject the null. What is your plain English conclusion?
"There is not enough evidence to say that Wellesley students have a mean height different from 64 inches."
You roll a six sided die 20 times. What’s the probability of getting exactly three 6’s?
23.79% (use the binomial formula)
Blood pressure in healthy individuals is normally distributed. The mean is 120 mm Hg with a standard deviation of 15 mm HG. What’s the probability of a healthy individual having a blood pressure between 110 and 130?
0.4972
You run a two-tailed test and get a test statistic of -2.15. At which of the following alpha levels would you be able to reject the null?
i. alpha = 0.10
ii. alpha = 0.05
iii. alpha = 0.01
You could reject when alpha = 0.10 and alpha = 0.05.
A charitable organization is running a raffle as a fundraiser. They sell 1000 tickets. There are ten third-prize tickets, two second-prize tickets, and a grand-winner ticket. A third-prize ticket gets you $20, a second-prize one gets you $100, and $500 goes to the grand winner. You buy a ticket. How much do you expect to win?
$0.90
Suppose you work for the Red Cross. Tomorrow you will collect blood from 32,000 donors. Based on demand, you need at least 1,850 of the donors to be O-negative. About 6% of people have blood type O-negative. What’s the probability that you will have enough O-negative donors show up tomorrow?
z = (0.0578 - 0.06)/0.001328 = -1.66
The area above this is 95.15% so that's your answer. (This question requires use of the CLT and Z-scores).
We learned in class that the lower alpha is, the less likely you are to make a type I error (if the null is true). If alpha goes down and the null is false, then your probability of making a type II error:
a. decreases
b. stays the same
c. increases
d. none of these (there's no way to know the impact)
c. increases