Unit 1: Univariate Data
The five number summary for a set of test scores is {32, 60, 75, 80, 99}
Does this data set contain any outliers? Explain with mathematical support!
No, Q1 - 1.5(IQR) = 30 which is the lower fence. 32 is the lowest value in our data set and therefore is NOT considered an outlier.
A sample of small cars was selected, and the values of x = horsepower and y = fuel efficiency was determined for each car. A linear regression model for this relationship is given here. Explain meaning of slope.
haty=44-0.15x
For each increase of 1 in horsepower, we expect the fuel efficiency of the vehicle to decrease by 0.15 on average.
A manufacturer of plastic cups used by restaurants would like to ensure that no more than 3% of their cups are defective. 300 cups manufactured by the company are chosen and checked for defects. State the population of interest.
ALL cups manufactured by this company.
P(A) = 0.4 and P(B) = 0.5. If A and B are independent, find P(A or B).
P(A or B) = 0.7
A random sample of 200 selected people showed that 40 of them thought of quitting their job sometime within the last month. Find a 90% confidence interval for the true proportion of people that have thought about quitting their job in the last month. [MUST SHOW FORMULA TO EARN POINTS!]
0.15348 to 0.24652
The mean of a data set is 35 while its median is only 28. Is this data set more likely to be skewed right, skewed left, or symmetric? Explain.
Because the mean > median, this data set is likely to be skewed right. The median is a resistant measure of center while the mean is not.
True or False? A negative residual indicates that a regression line overestimated the response variable.
TRUE
A library contains 30 bookshelves, each containing 100 books. The bookshelves are numbered 01-30 and two digits are selected at random. These correspond to the two bookshelves that will be chosen for our study. All books on these chosen shelves will be used in our study and will be checked for writing on them. What type of sampling is this?
Cluster Sampling
P(A|B) = 0.5 and P(B)=0.6 and P(A)=0.4
P(B|A) = ??
P(B|A) =3/4 = 0.75
Do the data below indicate evidence that the car accidents are evenly distributed throughout the days of the week? A week is selected at random and gives the following accident counts. Mon - 28 accidents, Tues - 32 accidents, Wed - 15 accidents, Thurs - 14 accidents, Fri - 38 accidents, Sat - 43 accidents, Sun - 19 accidents. Provide evidence.
The chi square test stat is 28.89 with p-value of nearly 0. We have strong evidence to suggest that the accident distribution throughout the week is NOT equal.
X follows a normal distribution with mean of 50 and unknown deviation. However we do know that 10% of the values are greater than 60. What was the standard deviation?
about 7.81
Calculate the correlation coefficient for the following set of points. (0, 40), (1, 35), (2, 36), (3, 33), (4, 30), (5, 31)
r = -.921
In order to perform an experiment using 60 members of a gym, I first divide the list of members into men and women because I feel that the results will be different based on gender. I then randomly choose 30 men and 30 women. I assign half of the men to the treatment group and half to the control group. I repeat this procedure with the women. This is an example of a:
A: block design.
B: completely randomized design
C: matched pairs design.
D: double-blind simple random sample.
E: factorial design.
A
The length in inches of a cricket chosen at random from a field is normally distributed with mean of 1.2 inches and standard deviation of 0.25 inches. Suppose 4 crickets are chosen at random, what is the chance that the sum of their lengths exceeds 5.6 inches?
0.0548
6 students were part of an experiment. Students were given a pre-test with 10 questions. Students were then given an online tutorial to watch. They then repeated the same test with 10 questions. Pretest Scores in order of Person 1 - 6: 7, 8, 5, 6, 6, 7 and Posttest Scores in order of Person 1- 6: 8, 8, 6, 7, 8, 6. Run the appropriate test to learn if the online tutorial can be thought to lead to significantly higher scores, on average. What is p-value for test?
p-value = 0.0873
Matched Pairs T-Test
NOT A TWO SAMPLE T-TEST!!
The mean of a data set is 40. It's IQR is 8. Suppose we transform the data by multiplying each value in the set by 2 and then adding 10. What will be the new mean and IQR for this transformed data set?
new mean = 90, new IQR = 16
A study recorded the number of beers consumed and the blood alcohol content (BAC) for 16 people of age 25. The correlation between these variables was found to be 0.8944. The average number of beers consumed by the group of 4.8125 with standard deviation of 2.1975. The average BAC was 0.07375 with standard deviation 0.0441. Find the slope of the LSRL.
slope = 0.0179 =
b_1=0.0179
An instructor would like to know if students enjoyed being in her class this year. She decides to interview a random sample of 30 of her students. She asks them if they enjoyed being in her class and then records their answers. She then finds the percent of students that enjoyed being in her class. What type of bias do you see present in this study, if any. Suggest a way to reduce this bias.
This suffers from RESPONSE BIAS. Students will likely feel they need to say they enjoyed it because the teacher is directly asking them. A better way to do this would be an anonymous survey.
30% of people eat candy every day of their life and are not ashamed to admit it [NOTE: Mrs. Stetter is one of them!]. Anyway, if we randomly select 40 people, what is the chance that at most 15 of them state that they eat candy every day?
0.8849
55 out of 80 randomly selected men and 48 out of 80 randomly selected women stated that they eat out more than once a week. Does this provide evidence the proportion of men eating out is significantly higher than the proportion of women that do? Show the z-test statistic used to run this test - formula and all values plugged and value.
z = 1.156
MUST have formula to get credit for this one!