Suppose I wanted to know whether a surprise quiz before the midterm improves your midterm score. Suppose I’m teaching two sections of this class, and I decide to test this by setting a surprise quiz for the first section and not for the second section, and then comparing the average scores of the two sections on the midterm. What assumption(s) would need to hold in order for me to estimate the true effect of a surprise quiz on midterm score in this manner? Explain.

Eyeglassomatic manufactures eyeglasses for different retailers. The number of days it takes to fix defects in an eyeglass and the probability that it will take that number of days are in the table. Table #5.1.8: Number of Days to Fix DefectsNumber of daysProbabilities

1 24.9%

2 10.8%

3 9.1%

4 12.3%

5 13.3%

6 11.4%

7 7.0%

8 4.6%

9 1.9%

10 1.3%

11 1.0%

12 0.8%

13 0.6%

14 0.4%

15 0.2%

16 0.2%

17 0.1%

18 0.1%

State the random variable.

b.)Draw a histogram of the number of days to fix defects

c.)Find the mean number of days to fix defects.

d.)Find the variance for the number of days to fix defects

. e.)Find the standard deviation for the number of days to fix defects.

f.)Find probability that a lens will take at least 16 days to make a fix the defect.

g.)Is it unusual for a lens to take 16 days to fix a defect?

h.)If it does take 16 days for eyeglasses to be repaired, what would you think?

A realistic estimate for the probability of an engine failure on a transatlantic fight is 1/14000. Use this probability and the binomial probability formula to find the probabilities of 0, 1, 2, and 3 engine failures for a three engine jet and the probabilities of 0, 1, and 2 engine failures for a two-engine jet. Carry all numbers to as many decimal places as your calculator will display. Use your results and assume that a fight will be completed if at least one engine works. find the probability of a safe fight with a three-engine jet(n=3) and find the probability of a safe fight with a two-engine jet(n=2). Write a report for the federal Aviation Administration that outlines the key issue, and include a recommendation. Support your recommendation with specific results.

Please note that for all problems in this course, the standard cut-off (alpha) for a test of significance will be .05, and you always report the exact power unless SPSS output states p=.000 (you’d report p<.001). Also, remember that we divide the p value in half when reporting one-tailed tests with 1 – 2 groups.

9. Paste the relevant SPSS output, including post hocs if necessary. (2 pts)

10. Create the most appropriate graph(s) for this data given the results. (2 pts)

11. Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and if relevant, effect size and/or post hoc analyses. Don’t forget to include a decision about the null hypothesis. (4 pts)

There are two routes to get from the student dorms to class - a long route, which is scenic, and a short route, which is not scenic. You want to study whether the route that the students choose to take is independent of the weather (in the context of the table, this will mean whether X and Y are independent), and you generate the accompanying table of probabilities.

Calculate E(X) and E(Y ).

(b) Calculate E(X | Y = 0). How is this different from E(X)?

(c) Are the route picked and the weather independent of each other? Why or why not? Use the numbers from the table to arrive at the answer.

1. A researcher developed a painkiller and wanted to test its effect. He recruited a group of 20 people who suffer from chronic pain of a similar level. Among these 20 participants, 10 participants received the painkiller and the other 10 participants received a placebo. One hour after taking the pills, the participants reported their pain level. For those who received the painkiller, the mean pain level was 4.8 and the standard deviation was 2.1. For those who received a placebo, the mean pain level was 5.5 and the standard deviation was 1.9. Can you conclude that the painkiller is effective? Perform an appropriate test at α = 0.01 with assuming that the homogeneity of variances assumption is satisfied.

• Which hypothesis test should be used?

 one-sample Z-test  one-sample t-test  independent-samples t-test  paired-samples t-test

• Step 1. State the hypotheses (both in words and in symbols)

• H₀: µ1 = µ2 (the paired sample means are equal)

• H₁: µ1 ≠ µ2 ("the paired sample means are not equal")

• Step 2: α = 0.01

• Find the critical value:

• Step 3: Calculate a test statistic and effect size (Cohen’s d). Show your work.
• Step 4: Make a decision.
• Step 5: State a conclusion (You should include the test statistic, p-value, effect size, and a verbal interpretation of the result).

Assume that the population of all sister-brother heights has a bivariate normal distribution and that the data below were sampled from this distribution.

Sister height (x) 69 64 65 63 65 62 65 64 66 59 62

Brother height (y) 71 68 66 67 70 71 70 73 72 65 66

Heights of n=11 pairs of siblings

(a) Consider the population of all sister-brother heights. Estimate the proportion of all brothers who are at least 5′ 10′′.

(b) Suppose that Carol is 5′ 1′′. Predict her brother’s height.

(c) Consider the population of all sister-brother heights for which the sister is 5′ 1′′. Estimate the proportion of these brothers who are at least 5′ 10′′.

find the expected value and the variance of the number of times one must throw a die until outcome 1 has occurred 4 times. This is the negative binomial distribution

Suppose we have three sets of random variables Wh, Xi, and Yj (for h= 1,...,k, i= 1,...,m, and j= 1,...,n) all of which are mutually independent. Assume that the three sets of random variables are all normally distributed with different means but the same standard deviation. The MLE for the means are just the group means and the MLE for the variance is the mean of the squared errors of the observations from the groups when taking into account the group means. Write a function to fit the this model to three observed data vectors w, x, y and return both the MLE and log-likelihood evaluated at the MLE. Use the commands

data("iris")

w = iris$Sepal.Width[iris$Sepecies=="setosa"]

x = iris$Sepal.Width[iris$Sepecies=="versicolor"]

y = iris$Sepal.Width[iris$Sepecies=="virginica"]

to make some data to analyze using your function. Compare the results from analyzing the data with the model for difference means to the results from analyzing the data when it would be assumed that the means are all the same. Comment on your results.

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there are 4 suits in the deck and 13 different values (ranks) per each suit). We refer to these 5 cards as a hand in the rest of this problem. Calculate the probability of each of the following events when dealing a 5-card hand at random. (a) Exactly one pair: This occurs when the cards have numeric values a, a, b, c, d, where a, b, c, and d are all distinct. (b) Exactly two pairs: This occurs when the cards have numeric values a, a, b, b, c, where a, b, and c are all distinct. (c) Only three of a kind: This occurs when the cards have numeric values a, a, a, b, c, where a, b, and c are all distinct. (d) Four of a kind: This occurs when the cards have numeric values a, a, a, a, b (clearly, b must be different from a because there are only 4 suits in the deck). (e) Full house: This occurs when the cards have numeric values a, a, a, b, b, where a and b are distinct. (f) Any of the scenarios above will lead to having at least a pair in the hand, and having at least a pair in the hand implies one of the events above must be true. Now, use the probabilities calculated in parts (a)–(e) to calculate the probability that we see at least a pair in the hand. Your answer has to be exactly 49.29%, ignoring rounding error.

Monthly rent at an apartment complex is $500. Operating costs follow a normal distribution with a mean of $15000 and a standard deviation of $300 (minimum of 0). The number of apartments rented follow a triangular distribution with a minimum of 30, most likely 34, and
a maximum of 40. Run the simulation and report the descriptive statistics for the profit of the complex (mean, etc.). Also, report percentile information on the level of profit. Finally, you are concerned that the complex might lose money in a typical month and you will be fired as a result. Should you be worried?

According to a report by the Commerce Department in the fall of 2004, 20% of U.S. households had some type of high-speed Internet connection. Let N_n denote the number of U.S. households with a high-speed Internet connection in n households. What is the probability that 20 of the first 200 households surveyed have high-speed Internet given that 5 of the first 75 households surveyed have it?

A probability experiment is conducted in which the sample space of the experiment is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}​,

event F={4, 5, 6, 7, 8}​, and event G={8, 9, 10, 11}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.

List the outcomes in F or G. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. F or G =_________

​(Use a comma to separate answers as​ needed.)

B. F or G =_________

Using the data below, calculate the appropriate test. Do this manually and show all steps. You can choose to do your working in the space here OR upload your working to the Dropbox in Blackboard. Show all steps to score full point.

The data reflects word retention for older adults with early onset Alzheimer's before a memory game was played and after the game was played.

A new online test preparation company compared 3,025 students who had not used its program with 2,150 students who had. Of those students who did not use the online test preparation program, 1,513 increased their scores on the SAT examination compared with 1,100 who did use the program. A significance test was conducted to determine whether there is evidence that the online test preparation company's students were more likely to increase their scores on the SAT exam. What is the p-value for an appropriate hypothesis test?