A professor has kept track of test scores for students who have attended every class and for students who have missed one or more classes. below are scores collected so far.
perfect: 80,86,85,84,81,92,77,87,82,90,79,82,72,88,82
missed 1+:61,80,65,64,74,78,62,73,58,72,67,71,70,71,66
1. Evaluate the assumptions of normality and homoscedasticity
2. conduct a statistical test to assess if exam scores are different between perfect attenders and those who have missed class
3. What is the meaning of the 95% confidence interval given from the R code. What does the 95% CI explain compared to the hypothesis test and how does the 95% CI relate to the test statistic and p value
In: Math
1. One‐Sample Univariate Hypothesis Testing of a Mean
Consider a random sample of 5 adults over the age of 25 from a large population, which is normally distributed, where E represents the total years of education completed: ? = [10, 12, 12, 16, 16] Suppose that someone claims that the average person in the population is a college graduate (? = 16).
A. What is the null hypothesis? What is the alternative hypothesis?
B. Can you reject the null hypothesis at the 10‐percent level of significance? Can you reject the null hypothesis at the 5‐percent level of significance? Use the critical value approach. You can use R for critical values, but you must show all of your calculations and explain. Use R, however, to check your work.
C. What is the 95‐percent confidence interval for years of education? Provide a written interpretation explaining your answer.
In: Math
As the director of the local Boys and Girls Club, you have claimed for years that membership in your club reduces juvenile delinquency. Now, a cynical member of your funding agency has demanded proof of your claim. Random samples of members and nonmembers are gathered and interviewed with respect to their involvement in delinquent activities. Each respondent is asked to enumerate the number of delinquent acts he/she has engaged in over the past year. The average number of admitted acts of delinquency are reported below. What can you tell the funding agency? Use an alpha of .01.
First, identify your (a) independent and (b) dependent variables.
Second, identify the (c) level of measurement for your independent variable and (d) the level of measurement for your dependent variable.
Third, (e) list out the steps of the 6 step traditional hypothesis test.
Fourth, (f) run a 6 step traditional hypothesis test.
(Conduct a 6 step traditional hypothesis test, find the p value).
Members 
NonMembers 

Mean 
10.3 
12.3 
Standard Deviation 
2.7 
4.2 
Sample Size 
40 
55 
In: Math
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 60.0 kg and standard deviation σ = 8.0 kg. Suppose a doe that weighs less than 51 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed
and released) at random in December is undernourished? (Round your
answer to four decimal places.)
(b) If the park has about 2500 does, what number do you expect to
be undernourished in December? (Round your answer to the nearest
whole number.)
does
(c) To estimate the health of the December doe population, park
rangers use the rule that the average weight of n = 60
does should be more than 57 kg. If the average weight is less than
57 kg, it is thought that the entire population of does might be
undernourished. What is the probability that the average weight
x
for a random sample of 60 does is less than 57 kg (assuming a
healthy population)? (Round your answer to four decimal
places.)
(d) Compute the probability that
x
< 61.2 kg for 60 does (assume a healthy population). (Round
your answer to four decimal places.)
Suppose park rangers captured, weighed, and released 60 does in
December, and the average weight was
x
= 61.2 kg. Do you think the doe population is undernourished or not? Explain.
Since the sample average is below the mean, it is quite likely that the doe population is undernourished. Since the sample average is above the mean, it is quite likely that the doe population is undernourished. Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished. Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.
In: Math
According to the Bureau of Labor Statistics (as of May 2016), the mean annual wage for criminal justice and law enforcement professors is $67,040. The median annual wage is $59,590. Explain how each would be calculated and the advantages to using each over the other to characterize the typical annual salary. As a professor, which should I view as more accurate/appropriate? Explain your position.
In: Math
Find all solutions to the following equations:
(a) √2x − 2 = √x + 1
(b) x4 − 5x2 + 6 = 0
(c) 3x − 7 < 5
(d) ax + b ≥ c
Explain step by step please
Suppose 4 is a right triangle with leglengths a and b and
hypotenuse
c. Find the missing side:
(a) a = 3, b = 4, c =?
(b) a = 12, c = 13, b =?
(c) a = 6, c = 9, b =?
2
In: Math
A certain type of tomato seed germinates 90% of the time. A gardener planted 25 seeds. a What is the probability that exactly 20 seeds germinate? b What is the probability that 20 or more seeds germinate? c What is the probability that 24 or fewer seeds germinate? d What is the expected number of seeds that germinate?
In: Math
AM vs PM Height (Raw Data, Software
Required):
It is widely accepted that people are a little taller in the
morning than at night. Here we perform a test on how big the
difference is. In a sample of 30 adults, the morning height and
evening height are given in millimeters (mm) in the table below.
Use this data to test the claim that, on average, people are more
than 10 mm taller in the morning than at night. Test this claim at
the 0.05 significance level.
(a) The claim is that the mean difference (x  y) is more than 10 mm (μ_{d} > 10). What type of test is this? This is a twotailed test. This is a lefttailed test. This is a righttailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t _{d} =(c) Use software to get the Pvalue of the test statistic. Round to 4 decimal places. Pvalue = (d) What is the conclusion regarding the null hypothesis? reject H_{0} fail to reject H_{0} (e) Choose the appropriate concluding statement. The data supports the claim that, on average, people are more than 10 mm taller in the morning than at night. There is not enough data to support the claim that, on average, people are more than 10 mm taller in the morning than at night. We reject the claim that, on average, people are more than 10 mm taller in the morning than at night. We have proven that, on average, people are more than 10 mm taller in the morning than at night. 
AM Height (x)  PM Height (y)  (x  y) 
1772  1763  9 
1413  1401  12 
1518  1511  7 
1622  1612  10 
1404  1397  7 
1489  1476  13 
1793  1780  13 
1567  1555  12 
1484  1473  11 
1639  1626  13 
1586  1571  15 
1633  1622  11 
1596  1584  12 
1423  1407  16 
1578  1567  11 
1541  1525  16 
1507  1492  15 
1473  1455  18 
1429  1420  9 
1492  1482  10 
1607  1599  8 
1769  1757  12 
1754  1746  8 
1632  1624  8 
1491  1484  7 
1505  1496  9 
1451  1438  13 
1662  1656  6 
1519  1509  10 
1649  1637  12 
In: Math
What is an example of a study that uses block randomization?
In: Math
Cognitivebased therapy (CBT) and familybased therapy (FBT) are two different treatments for anorexia. In an experimental study, fortysix anorexic teenage girls were randomly assigned to two groups. One group, consisting of n1 = 29 individuals, received CBT, and the other group, consisting of n2 = 17 individuals, received FBT. Weight of each individual is measured twice, once at the beginning and once at the end of the study period. The variable of interest is the weight change, i.e. weight after therapy minus weight before therapy. The data collected from the two samples are given below.
cognitive = c(1.7, 0.7, 0.1, 0.7, 3.5, 14.9, 3.5, 17.1, 7.6, 1.6, 11.7, 6.1,
1.1, 4.0, 20.9, 9.1, 2.1, 1.4, 1.4, 0.3, 3.7, 0.8, 2.4, 12.6, 1.9, 3.9,
0.1, 15.4, 0.7)
family = c(11.4, 11.0, 5.5, 9.4, 13.6, 2.9, 0.1, 7.4, 21.5, 5.3, 3.8, 13.4,
13.1, 9.0, 3.9, 5.7, 10.7)
Note that a positive weight change (weight gain) is generally good for anorexia patients. Let μ1 be the population mean weight change in the CBT group, and μ2 the population mean weight change in the FBT group. The goal is to conduct statistical inference on the difference μ1 − μ2

4. Twosample ttest relies on the assumption that the two samples are either large enough (n1 ≥ 30 and n2 ≥ 30) or coming from normal distributions. In the context of this problem, neither of the two samples is large enough.
(a) Check the normality assumption for both samples using the normal quantilequantile plot. Re member that you can do this in R using the qqnorm command.
(b) Suppose one thinks that the normality assumption does not hold for this data set, hence does not trust the results provided in the twosample ttest. Suggest a different hypothesis testing procedure that does not rely on the normality assumption. (Note: You don’t have to carry out the test.
In: Math
Data for the IFSAC Firefighter I examination test scores for two separate groups are found below. A random sample of firefighters is selected for each group. Group 1 attended the State Fire Academy for their training and Group 2 attended an inhouse academy. The groups are only tested once after they have received the training. All participants have no prior experience in the fire service. Assume normality of the populations.
Group 1 
Group 2 
99 
55 
89 
72 
80 
83 
91 
55 
79 
69 
61 
80 
54 
65 
54 
69 
52 
84 
66 
87 
50 
91 
72 
61 
64 
96 
89 
77 
53 
73 
83 
66 
100 
99 
1.Verify that assumptions are met (briefly list and explain)
2.Construct the hypotheses (null and alternative)
3.Formulate decision rule (calculate the pvalue or critical value)
4.Calculate the test statistic
5.Discuss your conclusion
Is there sufficient evidence that firefighters attending the inhouse academy have higher test scores on average than firefighters attending the State Fire Academy at the α=.05 significance level?
Is there sufficient evidence that the mean scores on the IFSAC Firefighter I examination test differ between the two groups at the α=.05 significance level?
In: Math
In: Math
In a test of the effectiveness of garlic for lowering cholesterol,
45
subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes
(beforeminus−after)
in their levels of LDL cholesterol (in mg/dL) have a mean of
5.2
and a standard deviation of
15.8.
Construct a 95%
confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
In: Math
Each of the distributions below could be used to model the time spent studying for an exam. Take one random sample of size 25 from each of the distributions below. Then, take 1,000 resamples (i.e., sample with replacement) of size 25 from your sample. In each case (a,b,c), plot the empirical distribution of the sample mean, estimate the mean of the sample mean, and estimate the standard deviation of the sample mean. Compare the results to the theoretical results.
a. N(5, 1.52)
b. Unif(0,10)
c. Gamma(5,1)
In: Math
1.
Counting the number of people who have been exposed to the Zika virus is an example of which of the following?
Continuous data
Discrete data
Quantitative data
Binary data
unanswered
2.Which type of bait catches the largest fish? A study was conducted using 3 different baits (worms, corn, and plastic lures), and the average weight of the fish caught was measured. What is the independent variable?
The type of bait
The weight of the fish
Corn
None of the above
3.
Which type of bait catches the largest fish? A study was conducted using 3 different baits (worms, corn, and plastic lures), and the average weight of the fish caught was measured. What type of variable is the dependent variable?
Continuous
Discrete
Qualitative
Binary
unanswered
4.
A study was conducted to determine if rats gain weight after experiencing different levels of exercise. Researchers used 24 rats, for three different levels of exercise, plus a control group. Rats were randomly assigned to each group until there were six rats per group. How many replications are there?
3
4
6
24
unanswered
5.
Which of the following are true when using the stratified sampling method? (Choose all that apply)
All subjects have and equally likely chance of being selected
Subjects are selected from each strata
Strata are usually created by convenience
All subjects are measured in the selected strata
unanswered
In: Math