The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = 0.000786 mm. Assume a random sample of 55 sheets of metal resulted in an x¯ = 0.3307 mm. Calculate the 98 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) The 98% confidence interval is from to

Suppose five bananas and seven oranges are placed in a fruit basket.

A. Suppose three fruits are chosen with replacement, sketch a tree diagram that shows all possible outcomes.

B. If three fruits are chosen at random with replacement find the probability that at least one banana is drawn.

C. If all three of the chosen foods are the same type what is the probability they’re all are bananas.

Suppose five bananas and seven oranges are placed in a fruit basket.

A. Suppose three are chosen without replacement sketch a tree diagram that shows all possible outcomes.

B. Add three fruits are chosen at random without replacement find the probability that the second group is an orange regardless of other draws .

C. It’s all three of the chosen fruit are the same type what is the probability they’re all oranges?

For three events A, B, and C, we know that

• A and C are independent,
• B and C are independent,
• A and B are disjoint,

Furthermore, suppose that ?(?∪?)= 2/3, ?(?∪?)=3/4,?(?∪?∪?)=11/12.

Find ?(?), ?(?), and ?(?).

In how many ways can 7 people { A, B, C, D, E, F, G } be seated at a round table if

(a) A and B must not sit next to each other;

(b) C, D, and E must sit together (i.e., no other person can sit between any of these three)?

(c) A and B must sit together, but neither can be seated next to C or D.

Consider each of these separately. For (c) you may NOT simply list all possibilities, but must use the basic principles we have developed (you may check your work with a list if you wish).

Hint: Conceptually, think of the groups of two or three people as one "multi-person" entity in the overall circular arrangement. However, a "multiperson" is an unordered entity, and you will have to think about how many ways a "multiperson" could be ordered. It may help to draw a diagram, fixing a particular person at the top of the circle (thereby eliminating the duplicates due to rotations).

The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.

43    41 39 39 38 37 37 36 34 33 33 32

The lower limit for determining outliers for a box-and-whisker plot is ________.

23.75

20.0

22.5

25.25

The two data sets in the table below are dependent random samples. The population of (x−y)(x-y) differences is approximately normally distributed. A claim is made that the mean difference (x−y)(x-y) is not equal to -23.5.

For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of the test statistic used in this test.

     Test statistic's value =

(b) Use your calculator to find the P-value of this test.

     P-value =

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.04 significance level. If there are two critical values, then list them both with a comma between them.

     Critical value(s) =

(d) What is the correct conclusion of this hypothesis test at the 0.04 significance level?     

• There is not sufficient evidence to support the claim that the mean difference is not equal to -23.5
• There is sufficient evidence to warrant rejection the claim that the mean difference is not equal to -23.5
• There is not sufficient evidence to warrant rejection the claim that the mean difference is not equal to -23.5
• There is sufficient evidence to support the claim that the mean difference is not equal to -23.5

The following contingency table shows the number of two-bedroom apartments grouped by monthly rent and location.

Monthly Rent                      York       Lancaster      Dover              Total
$600 to under $700              6              15                     9                      30
$700 to under $800              30                  21                   24                     75
$800 to under $900             15                  18                    12                      45
Total   51                   54                   45                     150

The probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 or is located in Lancaster is ________.

In a recent year, about two-thirds of U.S. households purchased ground coffee. Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a normal random variable with a mean of $75 and a standard deviation of $10.

a. Find the probability that a household spent less than $65.00.

b. Find the probability that a household spent more than $80.00.

c. What proportion of the households spent between $65.00 and $80.00?

d. 99% of the households spent less than what amount?

Show all work.

1. On a job interview you ask the employer what would the starting salary be. The interviewer says, "the average starting salary in my company will be $80,000."

You accept the job and find out your starting salary will be $30,000.

You and 6 co-workers have a starting salary of $30,000 while the CEO's son has a starting salary of $430,000! The average (mean) is $80,000.

You think this is a misuse of statistics because the employer should have used

a).a sample instead of the entire population (suspect samples)

b).a different average like the median (ambiguous average)

c). a lie detector

2.  

The mean of the grades: 100, 90, 100, 70, and 100.

is 92.

True or False

3. Match the key terms with their definitions.

a)the certainty that the observations in our sample group are accurate measures of the characteristics we set out to measure

b)a sample drawn from a population such that each and every member of the population has an equal chance of being included in the sample. Also, every sample of the same size has an equal chance of being selected.

c)being sure that our methods and presence in no way jeopardize our ability to use the random sample as a true representative of the population

d) another term for consistency

e) a convenient method of organizing raw data into a table, using classes

f) a way to display the distribution when we want to emphasize the categories' relation to the whole

1. Pie chart 2. Frequency Distribution 3. Reliability 4. External Validity 5. Internal Validity 6. Random Sample

Connor is a statistics student interested in the number of games won by each team per season during the past 12 years for a certain professional baseball league. He records the total number of wins x for each team each season and the probability of each value P(x), as shown in the table provided. Use Excel to find the mean and the standard deviation of the probability distribution. Round the mean and standard deviation to three decimal places. Number of wins, x P(x) 54 0.003 55 0.009 56 0.015 57 0.012 58 0.006 59 0.018 60 0.024 61 0.036 62 0.027 63 0.045 64 0.036 65 0.045 66 0.039 67 0.054 68 0.051 69 0.060 70 0.054 71 0.071 72 0.059 73 0.045 74 0.042 75 0.030 76 0.033 77 0.036 78 0.027 79 0.024 80 0.021 81 0.018 82 0.012 83 0.015 84 0.015 85 0.009 86 0.006 87 0.003

Problem Details:

A major beverage company needs forecasts of sales for next year. Quarterly sales data for the previous 13 years can be found in the “Beverage_Sales” worksheet of the Excel file titled Group Case #2 Data.

Requirements (You will NOT follow the PLAN-DO-REPORT algorithm. Address/answer all requirements in the order given.):

1. (2 points) Create a Time Series plot of the sales data. Briefly describe what you see in the plot.

2. (5 points) Develop a model to forecast sales for the four quarters of year 14.

3. (2 points) Forecast sales for the four quarters of year 14.

4. (4 points) Determine the MSE, MAD, MAPE for the model you developed in requirement #2. Using this information and any relevant information from the results of requirement #2, briefly discuss how accurate you think the forecasts for year 14 are.

Data:

57 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:

Round all your answers to 4 decimal places where possible.

The mean is:

The median is:

The sample standard deviation is: _______

The first quartile is: _______

The third quartile is: _______

What percent of the respondents have at least 7 pairs of Shoes? ______%

13% of all respondents have fewer than how many pairs of Shoes? __________

A class has 8 GSIs. Each GSI tosses a coin 20 times and notes the number of heads. What is the probability that none of the GSIs gets exactly 10 heads?

Q1- Identify each of the following statistics as either descriptive or inferential. For each, give a reason to support your response.

1 The average age of students in our statistics class is 20 years old.

2 The average age of undergraduate students in the CUNY system is 20 years old.

3 Seventy-three percent of sixth-graders have cell-phones.

4 The salary of LeBron James is greater than the average salary of his teammates.

5 Eighteen of the twenty three eighth-graders in Mr. Robson's algebra class have smart phones.

6 Less than 50% of all american households have two televisions.

Q2- Classify the following data as nominal, ordinal, interval or ratio. For each, give a reason to support your response.

1   Date of high-school graduation

2   The numbers on the Lakers' jerseys

3   Ranking of the planets by distance from sun

4   Distance of planets from sun

5   Height of children in an elementary school

6   Waiting number at DMV

7   Year at high-school

8   Weight of chickens at a poultry farm

9   Longitude of stars in the night sky

10 Social security number

TThe quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 108 hours. A random sample of 81 light bulbs indicated a sample mean life of 410 hours . a. Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment. b. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 410 hours? Explain. c. Must you assume that the population light bulb life is normally distributed? Explain. d. Suppose that the standard deviation changes to 80 hours. What are your answers in (a) and (b)?