The processing time for the shipping of packages for a company, during the holidays, were recorded for 48 different orders. The mean of the 48 orders is 10.5 days and the standard deviation is 3.08 days. Raw data is given below. Use a 0.05 significance level to test the claim that the mean package processing time is less than 12.0 days. Is the company justified in stating that package processing is completed in under 12 days?

1) Write Ho (null) and H1 (alternative) and indicate which is being tested

2) Perform the statistical test and state your findings; Write answer as a statement

1. A laboratory worker finds that 3% of his blood samples test positive for the HIV virus. In a random sample of 70 blood tests, what is the mean number that test positive for the HIV virus? (Round your answer to 1 decimal place)

2. A laboratory worker finds that 3% of his blood samples test positive for the HIV virus. In a random sample of 70 blood tests, what is the standard deviation of the number of people that test positive for the HIV virus? (Round your answer to 1 decimal place)

3.

In a certain college, 33% of the physics majors belong to ethnic minorities. If 8 students are selected at random from the physics majors, what is the probability that more than 5 belong to an ethnic minority?

a. 0.0187

b. 0.9154

c. 0.0846

d. 0.0659

4. Only 35% of the drivers in a particular city wear seat belts. Suppose that 20 drivers are stopped at random what is the probability that exactly four are wearing a seatbelt? (Round your answer to 4 decimal places)

5. Is the binomial distribution appropriate for the following situation:

Joe buys a ticket in his state’s “Pick 3” lottery game every week; X is the number of times in a year that he wins a prize.

a. yes

b. no

c. cannot be determined

Employees of Harvin & Co. are divided among the three divisons: Management and Administration, Machine Operations, and Maintenance. The following table shows the number of employees in each division, classified by gender.

                                                    Female           Male           Total

Mgmt & Administration           20                   11                   31

Machine Operators                    75                 125                 200

Maintenance                                  4                   16                    20

Total                                            99                 152                  251

Let A = a randomly chosen employee is a female,

      B = a randomly chosen employee is a male,

      C = a randomly chosen employee works in Management & Administration,

      D = a randomly chosen employee is a machine operator.

What is the approximate probability that a randomly chosen employee is a machine operator given that this person is a female?   

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you take the free samples offered in supermarkets? About 64% of all customers will take free samples. Furthermore, of those who take the free samples, about 41% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 309 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?
  

(b) What is the probability that fewer than 200 will take your free sample?


(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.41, while P(sample) = 0.64.


(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the probability of success calculated in part (c).

A number of restaurants feature a device that allows credit card users to swipe their cards at the table. It allows the user to specify a percentage or a dollar amount to leave as a tip. In an experiment to see how it works, a random sample of credit card users was drawn. Some paid the usual way, and some used the new device. The percent left as a tip was recorded and listed below. Using a = 0.05, what can we infer regarding users of the device?

Suppose that over a year the daily percent change (+ or -) for the S&P 500 adjusted closing value is approximately normally distributed with a mean of +0.03% and a standard deviation of 0.97%. Use this model to answer the following questions. Show all calculations. Show the standardization calculations.
a) For a randomly selected trading day, what the is probability that the percent change is less than +1.50%?

b) For what proportion of the trading days is the percent change between -2.00% and +2.00%?

c) What is the 3rd quartile of the percent change?

d) The 80th percentile?

A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach? This should be done in excel.

Suppose that a certain random variable, X, has the following cumulative distribution function (cdf):

F(x) = 0 x < 2

  0.25x2 – x + 1 2 ≤ x ≤ 4

1 4 < x

Find P(X > 2.5) (Round your answer to 4 decimal places)

M&M candies have 6 different color coatings in a standard single serving bag: blue, brown, green, orange, red and yellow. However, the number of each color that occurs in an individual bag may not be proportional. If bags of M&M Milk Chocolate candies contained proportional counts by color, there should be about 17% green M&M’s. A sample of M&M Milk Chocolate bags consisted of 1093 M&Ms. There were 273 green M&M’s of the total M&M’s in the sample. Determine with an acceptable error rate of 1% if our M&M sample is consistent with the equal color proportion of 17% green M&M’s. H0: p = 0.17 The percentage of green M&M’s in bags of Milk Chocolate M&M’s is 17%. HA: p  0.17 The percentage of green M&M’s in bags of Milk Chocolate M&M’s is not 17%. 8. What is the sample proportion for green M&M’s? (2 points) 9. What would be the value of the appropriate test statistic for this hypothesis test? (5 points) 10. What is the P-value of the test statistic determined in question #9? (5 points) 11. What would be the decision for this hypothesis test? (i.e. reject or do not reject the null hypothesis?) (4 points) 12. State your conclusion, based on the selected decision in question #11, appropriate to the hypothesis test on percentage of green M&M’s in M&M bags. (5 points) 13. If we wish to have a margin of error of 0.05 or less, at least how many M&M’s should we have had in our sample? (Was our sample large enough?) (4 points)

(a) Suppose you are given the following (x, y) data pairs. x: 1 2 6 y: 4 3 9 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x

(b) Now suppose you are given these (x, y) data pairs. x 4 3 9 y 1 2 6 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x

(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes No

(d) Solve your answer from part (a) for x (rounded to three digits after the decimal). x = + y Do you get the least-squares equation of part (b) with the symbols x and y exchanged? Yes No

(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts (a) through (d).

In general, switching x and y values produces the same least-squares equation.

In general, switching x and y values produces a different least-squares equation.

Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.

Use R studio to do it I need the code, thx.

Write your own function, called go_mean(). The user will provide a vector and the number of repetitions for the simulation. Your function should:
- Create an empty vector
- Draw a sample the same size as the vector, selecting from the vector itself, with replacement. - Compute the mean of the vector, and store it in the empty vector.

- Repeat the steps above n times.
- Compute an 80% confidence interval of the vector of means.
- Print the interval on the console so that it looks something like this: "Lower limit = value, Upper

limit = value", where the values are rounded to 2 decimal places.

Test your new function by creating a vector of 8000 z scores, and applying your function with 1000 reps

Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 5. Use the​ 68-95-99.7 rule to find the following quantities.

a. The percentage of scores less than 80 is​._____% ​(Round to one decimal place as​ needed.)

b. The percentage of scores greater than 85 is​.___%. ​(Round to one decimal place as​ needed.)

c. The percentage of scores between 70 and 85 is​.____%​ (Round to one decimal place as​ needed.)

Suppose a bridge has 10 toll booths in the east-bound lane: four are only for E-Z Pass holders, two are only for exact change, one takes only tokens, and the remainder are manned by toll collectors who accept only cash. During heavy-traffic hours it is difficult to see the signs indicating the type of toll booth. Suppose a driver selects a toll booth randomly.

• a. What is the probability that an exact-change toll booth is selected?

• b. What is the probability that a manual-collection toll booth or the token toll booth is selected?

• c. What is the probability that an E-Z Pass toll booth is not selected?

• d. Suppose the driver has only tokens. What is the probability of selecting the appropriate toll booth?

1. Explain what it means for the normal distribution to be symmetrical about the mean?

2. Why is it important to know the mean and standard deviation for a data set when applying the empirical rule?

3. If we are focused on 68% of the normal distribution, what percentage of the distribution is left in the upper tail only?

4. What value separates the 50% of the distribution from the other 50% of the distribution?