In a study of memory recall, 8 students from a large psychology class were selected at random and given 10 min to memorize a list of 20 nonsense words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later, as shown in the following table:

Subject 1 2 3 4 5 6 7 8

1 Hour 14 12 18 7 11 9 16 15

24 Hours 10 4 14 6 9 6 12 12

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3? Use a level .01 test.

A technical engineer is interested in understanding the battery life of two different laptops for student usage at a community college in California. The two models he has are Madroid and Krapple. He randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. Below is the data collected.

Does the technical engineer have statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life?

Provide the p-value from your analysis.

Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​salaries, do we know anything about the variation of salaries of TV personalities in​ general?

38
37
36
29
20
17
15
14
13.6
12.3

The range of the sample data is

​$nothing

million. ​(Type an integer or a​ decimal.)

The variance of the sample data is

nothing.

​(Round to two decimal places as​ needed.)

The standard deviation of the sample data is

​$nothing

million.

​(Round to two decimal places as​ needed.)

Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in​ general?

A.

​Yes, because the standard deviation is an unbiased estimator.

B.

​Yes, because the sample is random.

C.

​No, because there is an outlier in the sample data.

D.

​No, because the sample is not representative of the whole population.

5. A telephone sales solicitor, trying to decide between two alternative sales pitches, randomly alternated between them during a day of calls. Using approach A, 20% of 100 calls led to requests for the mailing of additional product information. For approach B in another 100 calls, only 14 % led to requests for the product information mailing.

.At the 0.05 significance level, can we conclude that the difference in results was due to chance?

- Construct the 95% confidence level for the difference between population proportions (π1 - π2).

- Identify and interpret the p-value for the test.

ANSWER MUST FOLLOW THIS FORMAT:

To prevent E. coli, meat should be cooked to an internal temperature of at least 160°F. However, different meat patties cooked for the same amount of time will have different final internal temperatures because of variations in the patties and variations in burner temperatures. A regional hamburger chain plans to replace its current burners with one of two new digitally controlled models. If there is a significant difference in the variance of the two models, the chain will select the model with the smaller variance in the final internal meat temperature. The chain's purchasing directors have arranged to randomly sample 11 patties cooked by burner model 1 and 13 cooked by burner model 2. The final internal temperature of the patties cooked on each burner are in cells F117 to G130 on the answers sheet.

- Perform a hypothesis test at the 10% significance level to see whether there is a significant difference between the variances of the two burner models.

DATA:

ANSWER MUST FOLLOW THIS FORMAT:

4. In order to test whether brand-name printer cartridges produce more printed pages, on average, than generic cartridges, a research firm has 6 randomly selected printer users use both types of cartridges and record how many pages were printed with each. The number of pages printed for each user by each type of cartridge are shown on the answers sheet in cells F92 to G98.

DATA:

ANSWERS MUST FOLLOW THIS FORMAT:

Do teachers find their work rewarding and satisfying? An article in Psychological Reports reported the results of a survey of a random sample of 395 elementary teachers and 266 high school teachers. Of the elementary school teachers, 224 said that they were very satisfied with their jobs, whereas 166 of the high school teachers were very satisfied with their work.

a. Based on this data, is it reasonable to conclude that the proportion of very satisfied teachers is different for elementary teachers than it is for high school teachers? Please state conclusion properly with context.

b. Construct and interpret a 95% Confidence Interval in the context of the above scenario.

c. How do the results in Part a and b compare? Do the results contradict each other?

In the mid-1990s, Colgate-Palmolive developed a new toothpaste for the U.S. market, Colgate Total, with an antibacterial ingredient that was already being successfully sold overseas. At that time, the word antibacterial was not allowed for such products by the Food and Drug Administration (FDA). In response, the name “Total” was given to the product in the United States. The one word would convey that the toothpaste is the “total” package of various benefits. Young & Rubicam developed several commercials illustrating Total’s benefits and tested the commercials with focus groups. One commercial touting Total’s long-lasting benefits was particularly successful. The product was launched in the United States in January of 1998 using commercials that were designed from the more successful ideas of the focus group tests. Suppose 32% of all people in the United States saw the Total commercials. Of those who saw the commercials, 40% purchased Total at least once in the first 10 months of its introduction. According to U.S. Census Bureau data, approximately 20% of all Americans were in the 45-64 age category. Suppose 24% of the consumers who purchased Total for the first time during the initial 10-month period were in the 45-64 age category. Within three months of the Total launch, Colgate-Palmolive grabbed the number one market share for toothpaste. Ten months later, 21% of all U.S. households had purchased Total for the first time. The commercials and the new product were considered a success. During the first 10 months of its introduction, 43% of those who initially tried Total purchased it again.   

1. What percentage of U.S. households purchased Total at least twice in the first 10 months of its release?

2. Can you conclude the initial purchase of Total was independent of age? Use a quantitative argument to justify your answer.

3. Calculate the probability that a randomly selected U.S. consumer is either in the 45-64 age category or purchased Total during the initial 10-month period.

4. What is the probability that a randomly selected person purchased Total in the first 10 months given that the person is in the 45-64 age category?

e. What percentage of people who did not see the commercials purchased Total at least once in the first 10 months of its introduction?

A multiple-choice test has 48 questions, each with four response choices. If a student is simply guessing at the answers,

1. What is the probability of guessing correctly for any individual question?

2. On average, how many questions would a student answer correctly for the entire test?

3. What is the probability that a student would get more than 15 questions correct? p(more than 15 answers correct)

4. What is the probability that a student would get 15 or more questions correct simply by guessing?

You want to test a new instrument for ammonia analysis in fog water (basic fog is associated with uncontrolled ammonia releases from waste lagoons containing agricultural waste from confined animal feedlot operations or CAFOs). First you have to check its operation against a standard reference solution of 100.00 micromolar ammonia. It reads 98.23, 88.16, 101.30, 101.47, 99.59 and 101.66 over six replicate measurements. Using α = 0.05 and a t-test, solve for if there is any evidence that the analysis is giving inaccurate results? Show your work. If the results are inaccurate you must express the bias (positive or negative) for the technique.

PLEASE NUMBER EACH ANSWER

Students will use advanced looping methods including replicate(), lapply(), sapply(), and apply(), and access datasets provided with R packages in an R script.

1. The function call, rnorm(1), generates a normal random number. Use replicate() to generate 10 normal random numbers and assign them to a vector called nums.
   
2. The R statement, data(iris), loads the built-in R data set iris. This dataset has 150 rows and 5 columns. The 5 column names are "Sepal.Length","Sepal.Width","Petal.Length","Petal.Width" and "Species".
   1. Write R code(s) to return a list of 4 items that correspond to the averages of the first 4 columns in iris. The contents of the list should be as follows:
      
      $Sepal.Length
      [1] 5.843333
      
      $Sepal.Width
      [1] 3.057333
      
      $Petal.Length
      [1] 3.758
      
      $Petal.Width
      [1] 1.199333
      
3. With the iris dataset still loaded,
   1. write R code(s) to return a vector of 4 items that correspond to the averages of the first 4 columns in iris. The contents of the vector should be as follows:

4. The following R code converts the contents of the first 4 columns in iris to a matrix called data.
   data=as.matrix(iris[,1:4])
   1. Write R code(s) to use apply() to return a vector that contains the max values of the 4 columns. The contents of the vector should be as follows [Hint, use max()]:

5. Write R code(s) to read the contents of the provided file COS-206-ShoppingCart.html into a variable called cart and then show the first 5 lines of cart.

25. An important application of regression in manufacturing is the estimation of cost of production. Based on DATA from Ajax Widgets relating cost (Y) to volume (X), what is the cost of producing 600 widgets?

Xander, summer statistics intern in the Superintendent’s Office for the Palisades Point School District, wonders if the homerun teacher referrals in the 7^th grade for two week periods are comparable. He tests this claim very preliminarily at the 1% significance level as a pilot study, and presumes that the distribution of referrals among these teachers is reasonably normal. He collects independent, simple random samples. The following data tables represent the numbers of referrals made by these seventh grade teachers:

What hypotheses should he test? Were the results statistically significant? What conclusion should he draw, qualifying the result as extreme or marginal if appropriate? Explain his anticipated findings in detail, both technically and contextually. Be sure to identify the necessary critical and p-values as part of the analysis.

Listed below are measured amounts of caffeine​ (mg per 12oz of​ drink) obtained in one can from each of 14 brands. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are the statistics representative of the population of all cans of the same 14 brands​ consumed?

49
40
34
30
0
34
33
59
56
39
46
53
0
0

The range of the sample data is

nothing

▼

brands squared .brands2.

mg per 12 oz of drink.mg per 12oz of drink.

left parenthesis mg per 12 oz of drink right parenthesis squared .(mg per 12oz of drink)2.

brands.brands.

​(Round to one decimal place as​ needed.)

The standard deviation of the sample data is

nothing

▼

mg per 12 oz of drink.mg per 12oz of drink.

left parenthesis mg per 12 oz of drink right parenthesis squared .(mg per 12oz of drink)2.

brands squared .brands2.

brands.brands.

​(Round to one decimal place as​ needed.)

The variance of the sample data is

nothing

▼

brands.brands.

mg per 12 oz of drink.mg per 12oz of drink.

left parenthesis mg per 12 oz of drink right parenthesis squared .(mg per 12oz of drink)2.

brands squared .brands2.

​(Round to one decimal place as​ needed.)

Are the statistics representative of the population of all cans of the same 14 brands​ consumed?

A.

The statistics are likely representative of the population of all cans of these brands that are consumed because the results from any sample of the 14 brands will be typical of the population.

B.

The statistics are not necessarily representative of the population of all cans of these brands that are consumed because each brand is weighted equally in the calculations. It is unlikely that each of the 14 brands of soda are consumed equally.

C.

The statistics are not necessarily representative of the population of all cans of these brands that are consumed because it is necessary to have at least 5 of each brand in order to get a sample that is representative of the population.

D.

The statistics are likely representative of the population of all cans of these brands that are consumed because each brand is being represented in the sample.

Click to select your answer(s).