Units 1-2
A ________ is how many standard deviations away from the mean an observation is.
What is a z-score?
When two event have no outcomes in common, they are referred to as __________________ events
What is mutually exclusive?
This is a number that is computed from sample data.
What is a statistic?
The ______ hypothesis is the original claim, while the _______ hypothesis is the claim that you find evidence for.
What is null, alternative?
This happens to a t-distribution when the degrees of freedom increases.
Center =
Area in the tail =
What is constant, decreases?
_________ are characteristics of individuals, they may take on different values of different kinds of themselves.
What are variables?
Label these 4 processes of a completely randomized design in order from start to end:
Randomly assign subjects
Compare results
Identify the sample
Identify the treatments
Identify the sample -> Randomly assign subjects -> Identify the treatments -> Compare results
At a national convention attended by many educators, about 30 percent of the attendees are from the northeast. Of all the attendees of the national convention, 25 will be selected at random to receive a free book. What would be the mean and standard deviation of the sampling distribution of the proportion of attendees for samples of size 25?
The mean would be 0.3 and standard deviation will be 0.091
√0.3(0.7)/25 = 0.091
In a hypothesis test for a single proportion, this is assumed for the calculation of the p-value.
What is a true null hypothesis?
A sociologist recorded the number of contacts entered in a cell phone and the number of texts sent in a week for 20 cell phone users. The resulting data were used to conduct a hypothesis test to investigate whether there is a linear relationship between the number of contacts and the number of texts sent. What will be the correct hypotheses for the test?
What is
H0: B1 = 0
Ha: B1 ≠0
An agricultural economist says that the correlation between corn soy bean prices is r = 0.7. This means that:
(A) when corn prices are above average, soybean prices also tend to be above average.
(B) there is almost no relation between corn prices and soybean prices.
(C) when corn prices are above average, soybean prices tend to be below average.
(D) when soybean prices go up by 1 dollar, corn prices go up by 70 cents.
(E) the economist is confused, because correlation makes no sense in this situation.
Correct Answer:
(A) when corn prices are above average, soybean prices also tend to be above average.
Identify the correct sampling method and relationship
Researchers wanted to see if sleep deprivation caused a decrease in mental performance. They gathered 20 volunteers and randomly assigned half to a sleep deprivation cycle and half to a regular sleep cycle. After two sleep cycles, researchers will examine how quickly the subjects can complete a maze.
What is random assignment?
What is cause-and-effect?
Recipes for the same type of cookies can vary in terms of ingredients and baking times. From a collection of chocolate chip cookie recipes, a baker randomly selected 5 recipes. From a collection of oatmeal raisin cookie recipes, the baker randomly selected 4 recipes. The mean baking times, in minutes, for each sample were recorded as x̄C and x̄O.
What is the correct unit of measure for the standard deviation of the sampling distribution of x̄C − x̄O?
Minutes squared, Recipes, Number of raisins, Minutes, or Number of chocolate chips?
What is minutes?
Researchers are testing a new diagnostic tool designed to identify a certain condition. The null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. For the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective.
___________ the significance level to ___________ the probability of Type I error.
What is decrease, decrease?
A recent study of 1,215 randomly selected middle school students revealed that the average number of minutes they spent completing homework during the school week was 180 minutes with a standard deviation of 45 minutes. This will be the the standard error, in minutes, the sampling distribution of the mean number of minutes spent on homework per week for all middle school students?
What is 45 /√1,215
s /√n
To represent distributions, graphs take these following shapes (state all to get it correct):
Symmetric, skewed (left or right), unimodal, bimodal, and uniform.
An experiment compared the adhesion of 2 types of paint, A and B, to 3 types of metal, 1, 2, and 3, used in automobiles. Thirty sheets of metal were used in the experiment: 10 of Metal 1, 10 of Metal 2, and 10 of Metal 3. Half of each metal type will receive paint A and the other half will receive paint B. The adhesion of the paints was measured, and the measures were compared. How many experimental units are in the experiment?
There are 30 experimental units in the experiment.
Suppose a large local bakery sells cupcakes, and historically, 20% of the cupcakes sold are chocolate flavored. Imagine taking an SRS, from all the cupcakes they make in a day, of 50 cupcakes from the bakery.
Given the mean of the sampling distribution of p̂ is 0.20, this would be the standard deviation of the same sampling distribution.
What is 0.0566?
Op̂ = √0.2(1-0.2)/50
= 0.0566
A random sample of 500 adults living in a large county was selected and 304 adults from the sample indicated that the unemployment rate was of great concern. What is the standard error of the sample proportion p̂?
What is √(0.61)(0.39)/500?
or 0.022
Jana, a high school principal, hosted a movie event at her school. Jana's assistant kept track of the number of students in each grade who attended the event. The distribution shown in the table represents the number of students in each grade that were present. Jana knows that the grade levels are equally distributed across the school of 1,200 students. She would like to use a chi-square test to see if the proportion of individuals in each class at the movie are also equally distributed. This will be the number of seniors expected at the event.
What is 59.5?
Constant: Coefficient = -42.734, S.E of Coeff = 2.717
Waist: Coefficient = 1.70, S.E of Coeff = 0.0743
A) Write the equation of the regression line.
B) One of the men who participated in the study had a waist size of 35 inches and 10% body fat. Calculate the residual associated with the point for this individual.
A) ŷ = -42.734 + 1.7x
B) ŷ = -42.734 + 1.7(35)
ŷ = 16.766 Residual = 10 - 16.766
= -6.766%
According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W ?
What is 4.11?
√np(1-p) = √300(0.06)(0.94)
= 4.11
A study reported that finger rings increase the growth of bacteria on health-care workers’ hands. Research suggests that 31 percent of health-care workers who wear rings have bacteria on one or both hands, and 27 percent of health-care workers without rings have bacteria on one or both hands. Suppose that independent random samples of 100 health-care workers wearing rings and 100 health-care workers not wearing rings are selected. This is the standard deviation of the sampling distribution of the difference in the sample proportions (wear rings minus does not wear rings) of health-care workers having bacteria on one or both hands?
What is 0.064?
σp̂1 - p̂2
√0.31(0.69)/100 + 0.27(0.73)/100
A farmer wants to investigate whether a new pesticide will decrease the proportion of pumpkin plants that are being eaten by bugs in the farmer’s pumpkin patches compared to the current pesticide being used. The farmer applied the old pesticide to patch A and the new pesticide to patch B. Let pA represent the proportion of pumpkin plants eaten by bugs in patch A and pB represent the proportion of pumpkin plants eaten by bugs in patch B. This will be the correct null and alternative hypotheses to test whether the new pesticide results in fewer pumpkin plants eaten by bugs?
What is
H0: pA = pB
Ha: pA > pB
Assuming all conditions for inference are met, which of the following defines a 95 percent confidence interval for the slope of the least-squares regression line?
A. 1.321(0.945)
B. 1.717(0.22)
C. 1.717(0.023)
D. 1.321(0.023)
What is C: 1.717(0.023)?
t*(SEb1 )
SEb1 = 0.023
90% conf. int. - t* = 1.717