##### A professor has kept track of test scores for students who have attended every class and...

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...

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...

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 Non-Members 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...

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...

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)...

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

Suppose 4 is a right triangle with leg-lengths 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 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...

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 (μd > 10). What type of test is this? This is a two-tailed test. This is a left-tailed test.     This is a right-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t d = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0     (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?

What is an example of a study that uses block randomization?

In: Math

##### Cognitive-based therapy (CBT) and family-based therapy (FBT) are two different treatments for anorexia. In an experimental...

Cognitive-based therapy (CBT) and family-based therapy (FBT) are two different treatments for anorexia. In an experimental study, forty-six 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. Two-sample t-test 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 quantile-quantile 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 two-sample t-test. 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....

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 in-house 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 p-value or critical value)

4.Calculate the test statistic

Is there sufficient evidence that firefighters attending the in-house 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

##### if we assume that the degree of freedom is fixed as an absolute value of the...

if we assume that the degree of freedom is fixed as an absolute value of the T-Stat gets bigger what happens to the corresponding P value

In: Math

##### In a test of the effectiveness of garlic for lowering​ cholesterol, 45 subjects were treated with...

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...

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...

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

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

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

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