Stats Final Review
Where is the 10th percentile of the Z distribution?
-1.28
Which of the following p-values gives you the most evidence against Ho? That is, which one is most likely to reject Ho?
.002
Which significance level (alpha) do we use in our class when we do our hypothesis test?
.05
A fair coin (one for which the probability of heads and the probability of tails are 0.5) is tossed 6 times. The probaility that less than 1/3 of the tosses are heads is
0.1094
The standard deviation of the outcome of one die roll was found in lecture to be 1.71. What is the standard error of the average when you roll 100 die?
0.171
What is P(0 < Z < 1)? (round to 2 decimal places)
0.34
Using our rule from class (see lecture notes), approximately what proportion of the data from a normal distribution is within two standard deviations on either side of the mean? Choose the best answer.
0.95
Suppose that 40% of all adults in Ohio support an increase in sales tax. A survey asks a random sample of 10 adults in Ohio if they support an increase in the state sales tax. Let X denote the number in the sample that say they support the increase. What is the standard deviation of X?
1.55
Suppose X has a normal distribution with mean 10 and standard deviation 2. If Z = 0, then X must be equal to
10
The standard deviation of a binomial distribution with n=100 and p=.20 is
20
Suppose a 95% confidence interval for the population mean turned out to be 30±5. What is the value of the sample mean that was used to calculate this confidence interval?
30
Suppose a 95% confidence interval for the population mean turned out to be 30±5. If you increase the confidence level to 98% and keep everything else the same, which of the following results is possible?
30 ± 10
Suppose a 95% confidence interval for the population mean turned out to be 30±5. If you increase the sample size and keep everything else the same, which of the following results is possible?
30±2
Suppose a 95% confidence interval for the population mean turned out to be 30±5. What is the margin of error for this confidence interval?
5
Suppose the percentage of females who support a casino in Columbus is 55%. If supporting a casino in Columbus is not related to gender, what percentage of males support a casino in Columbus?
55%
If the Z-value is 1.96, and X has a normal distribution with mean 60 and standard deviation 6, what X-value corresponds to this Z-value?
71.76
The time (X) to complete a standardized exam is approximately normal with mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?
78.4 minutes
Which of the following statements about correlation is true? (select all that apply but note, there may be only one correct choice.)
incorrect Response If X and Y have a strong correlation then X and Y have a cause and effect relationship. incorrect Response If you switch X and Y the correlation will change. incorrect Response If you change the units for X and Y the correlation will change. Correct Answer Correlation measures the strength and direction of a linear relationship.
The distribution of all possible sample means from all possible samples of size n from the population is called the
sampling distribution of the sample mean
μX =
the mean of the random variable X
If P(A)=.35 and P(B)=.5 then P(A and B) is
Cannot be determined from the information given
If P(A and B)=0, P(A)=0.20, P(B)=0.80, then A and B are
Disjoint
Which of the following is not a characteristic of a binomial experiment?
Each trial results in two or more outcomes.
A correlation of -1 means there is a very weak correlation between X and Y.
False
A survey is conducted to study the backgrounds of professional golfers in the United States. A random sample of 300 professional golfers was surveyed. One question that was asked was: "Did your parents play golf?" 10% of the golfers said yes. True or False: The population for this survey is all people in the United States
False
If you reject Ho there is no chance that Ho can be true.
False
P(Z > -2.00)=0.0228
False
P(Z=1.00) is 0.8413
False
When finding correlation, it matters which variable is X and which variable is Y.
False
s a general rule, the normal distribution is used to approximate the binomial distribution as long as n times p times (1-p) is greater than or equal to 10.
False
Suppose you are predicting exam score using study time (hours), and your regression line is Y=20+10X. Assume the line fits well. Interpret the slope in this case.
For every additional hour of study time, the exam score is predicted to increase by 10 points.
A pizza delivery company claims that they deliver their pizzas in 15 minutes on average. You believe it is more than that. You conduct a hypothesis test. What is the alternative hypothesis?
Ha: μ > 15
Someone claims that the population mean is 10, but you beleive it is more than 10. Which of the following is the null hypothesis?
Ho: μ =10
Suppose you estimate the average pizza delivery time for Joe's Pizza Shack to be 20 minutes plus or minus 3 minutes using a 95% confidence interval. Joe's Pizza Shack claims in their advertisements that their average pizza delivery time is 15 minutes. Based on your confidence interval do you believe their claim?
No
The Binomial Random variable is a discrete random variable with infinitely many possible values.
No, the number of successes cannot exceed the number of trials
Suppose you want to estimate the average number of hours that children spend outside per day. Which of the following techniques would you use?
Confidence interval for μ
Which of the following is true about μX-bar
μX-bar equals μX
The notation for the standard error of X-bar is
σX-bar
The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. What percentage of the students take longer than 80 minutes to finish?
15.87%
Suppose it is projected that 75% of all Americans aged 18-24 will vote in the 2016 Presidential election. You take a random sample of 1,000 American students 18-24 years old, and count the number who will vote (call it X). What is the variance of X?
187.5
As the sample size increases, what happens to the standard error of X-bar?
It decreases
Suppose a 95% confidence interval for the population mean turned out to be 30±5. If you now use a sample size that is 4 times larger than the one you had before, how would your margin of error be affected? (Be careful on this one!)
It would be cut in half
Suppose two people used two different data sets of two different sizes to estimate a population mean. (Assume the population standard deviation is the same in both cases.) The first person made a 95% confidence interval from their data, and the 2nd person made a 90% confidence interval from their data. Which of the following MUST be true?
The first person's CI has a larger MOE The second person's CI has a larger MOE They both have the same MOE Correct Answer Can't tell from the information given
Every regression line must pass through the point that contains both the mean of X and the mean of Y.
True
It is possible for a data set to have both a correlation of 1, and a regression line with a slope of 2.
True
Jim and John go to a coffee shop during thier lunch break and toss a fair coin to see who will pay. The probability that John will pay 3 days in a row is 0.125
True
Suppose the regression line fits well, the minimum X value is 1 and the maximum X value is 10. This means for any X value between 1 and 10 you can make a prediction for Y.
True
When finding the best regression line, it matters which variable is X and which varaible is Y.
True
If a statistician does not have enough evidence against Ho, what do they conclude?
"I cannot reject Ho"
A newspaper claims that the average number of hours that teenagers spend playing video games per week is 10. You believe it is higher than that. You take a sample of 100 teenagers and their average video game time is 11.5 hours. What is the null hypothesis?
Ho: μ =10
Suppose you roll a die 100 times and find the probabability that the average is less than 3. Then you roll a die 200 times and find the probability that the average is less than 3. Which scenario will give you the smallest probability?
Rolling the die 200 times give you a smaller probability that the average is less than 3.
A researcher wants to estimate the average age at which people develop a certain disease. She takes a random sample of 500 patients with the disease and finds the average age at which they developed the disease was 62 years with a standard deviation 3.5 years. What is the statistic in this problem?
The avereage age at which the people in the sample developed the disease (62 years)
If you are doing a hypothesis test for the population mean, which of the following is the formula for the test statistic?
Xbar-Mu / Sigma/radical n
Suppose you want to find the probability regarding X-bar. When do you need the Central Limit Theorem?
You use the Central Limit Theorem if X does not have a normal distribution and n>30.
The standard error of X-bar measures
the standard error of all possible values of x (SD/square root of n)
The margin of error for a confidence interval includes the amount of bias that occurred in the data.
False
The slope and the correlation are NEVER equal.
False
To find R-squared(r2), you simply take the square root of r.
False
When two variables X and Y decrease together, we describe the nature of their association as a negative linear relationship.
False
Suppose that stat exam scores have a normal distribution with mean 80 and standard deviation of 5, and math exam scores have a normal distribution with mean 80 and standard deviation of 10. Bob scores 90 on both exams. How did Bob do on these exams compared to his classmates in each case?
Bob did better on the stat exam than the math exam, compared to his classmates
Say X has a binomial distribution. Let the probability of success p=0.2. You take a random sample of 50 and want to know the probability that you will have more than 20 successes. What is your first step?
Check conditions to make sure you can use the Normal approximation to the Binomial distrubtion.
For regression, if you switch X and why what will be impacted. (select all that apply)
Correct Answer Slope
A correlation of 0.81
Correct Response ensures a strong, positive, linear relationship. Correct Answer Incorrect Response indicates there may be a trong positive linear relationship, but we don't know without looking at the graph
R-squared (r2) measures the percentage of data points that lie directly on the regresion line.
False
Suppose a recent survey found that the amount of vitamin C people report taking daily is strongly negatively correlated with the number of colds they report getting in a given year. You can conclude from this that vitamin C causes a reduction in colds
False
Suppose the regression line fits well, the minimum X value is 1 and the maximum X value is 10. This means for any X value between 1 and 10 you can calculate a residual.
False
The Y-intercept of the regression line always has a meaningful interpretation.
False
The correlation between test grade and hours studying is 0.65. If we change the units of study time from hours to minutes, then to get the new correlation we need to multiply (60)*(0.65).
False
You are interested in the average number of hours that adults spend on the internet per week. Bob claims that the average is 10 but you believe its it higher than that. You conduct a hypothesis test for the population mean and you end up rejecting Ho. Bob says "OK, you reject the hypothesis that the population mean is 10. So what do YOU think the population mean is?" How do you respond to Bob?
You use your data and calculate a 95% confidence interval for the population mean.
