3. A pharmacy is using X bar and R charts to record the time it takes to fill a prescription after the customer has turned in or called in the prescription. Each day, the pharmacy records the times it takes to fill six prescriptions. During a 30-day period, the hospital obtained the following values: X double bar = 20 minutes; R bar = 4 minutes. The upper and lower specifications are 23 minutes and 13 minutes respectively. What is the value of Cpk, to two decimal places?

The correlation between X and Y ______________.

Question options:

Question 2

The residual represents the discrepancy between the observed dependent variable and its _______ value.

Question options:

A research team conducted a study showing that approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight


(b) more than two ties are too tight


(c) no tie is too tight


(d) at least 18 ties are not too tight

Let X ∼ Pois(4), Y ∼ Pois(12), U ∼ Pois(3) be independent random variables.

1. a) What is the exact sampling distribution of W = X + Y + U?

2. b) Use R to simulate the sampling distribution of W and plot your results. Check that the simulated mean and standard error are close to the theoretical mean and standard error.

3. c) Use the simulated sampling distribution to estimate P(W ≤ 14) and then check your estimate with an exact calculation.

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

To demonstrate flavor aversion learning (that is, learning to dislike a flavor that is associated with becoming sick), researchers gave one group of laboratory rats an injection of lithium chloride immediately following consumption of saccharin-flavored water. Lithium chloride makes rats feel sick. A second control group was not made sick after drinking the flavored water. The next day, both groups were allowed to drink saccharin-flavored water. The amounts consumed (in milliliters) for both groups during this test are given below.

(a) Test whether or not consumption of saccharin-flavored water differed between groups using a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)

(b) Compute effect size using eta-squared (η²). (Round your answer to two decimal places.)
η² =

You have been talking to a student from the engineering program at UBC who has also taken up temporary residence at the North Pole in between active semesters of her studies. Because of her engineering background, the elves have given her the nickname “Casey Jones”. Casey scoffs at the α = .05 significance level that psychologists use in their hypothesis testing procedure. She tells you “That means you will, in the long run, make an error one time in twenty. If engineers had an error rate like that think of all the buildings and bridges and such that would be falling down! Why don’t you psychologists be more like engineers and set your error rate to something like one in a million instead of one in twenty?” Explain to Casey Jones why, in the context in which psychologists use it, an alpha level of one in twenty makes more sense than an alpha level of one in a million.

Meiosisis the process in which a diploid cell that contains two copies of the genetic material produces an haploid cell with only one copy (sperms and eggs). The resulting molecule of genetic material is linear molecule that is composed of consecutive segments: a segment that originated from one of the two copies followed by a segment from the other copy and vice versa. The border points between segments are called points of crossover. The Haldane model for crossovers states that the number of crossovers between two loci on the genome has a Poisson(λ) distribution. Assume that the expected number of crossovers between two loci in a fixed period of time is 2.25.The next 3 questions refer to this model for crossovers. (The answer may be rounded up to 3 decimal places of the actual value.)

1. The probability of obtaining exactly 4 crossovers between the two loci is

2. The probability of obtaining at least 4 crossovers between the two loci is

3. A recombination between two loci occurs if the number of crossovers is odd. The probability of recombination between the two loci is, approximately, equal to ??? (Compute the probability of recombination approximately using the function "dpois". Ignore odd values larger than 9)

Q3. Hypothesis: Informing people about recycling causes them to recycle more.

Study design: 50 households were randomly assigned to a treatment group where they were

informed by letter about proper recycling habits and its benefit on environment, while 50

different households were randomly assigned to a control group that did not receive such a letter.

After 3 months, the weekly average recycling amount in the treatment group was 12.4 lbs (

sd

=

2.5), while the weekly average recycling amount in the control group was 3.7 lbs (

sd

= 1.1)

d. Determine the appropriate test: z-test or t-test. Explain why you chose that test.

e. Calculate the appropriate test statistic

f. Decide whether you should reject the null hypothesis.

Think about a population mean that you may be interested in and propose a confidence interval problem for this parameter. Your data values should be approximately normal.

For example, you may want to estimate the population mean number of hours people watch tv each week. Your data could be that you spoke with seven people you know and found that they went out 14,20,17,26,2,12, and 16 times last week. You then would choose to calculate a 95% (or another level) confidence interval for the population mean.

Assume a random sample was chosen, which is required to determine a confidence interval.

please show all steps in the solution

Answer the questions below using the appropriate statistical technique. For questions involving the use of hypothesis testing, you must:

1. State the null and research hypotheses

2. Provide the Z(critical), T(critical), or χ 2 (critical) score corresponding to the α threshold for your test

3. Provide your test statistic

4. Provide your decision about statistical significance

A random sample of 350 persons yields a sample mean of 105 and a sample standard deviation of 10. Construct three different confidence intervals to estimate the population mean, using 95%, 99%, and 99.9% levels of confidence. What happens to the interval width as the confidence level increases? Why?

You must also substantively interpret the results of your test (but keep it short). That is, don’t just focus on whether or not a test is statistically significant, but also briefly comment on what the result actually means. You may find it helpful to proceed using the five-step model, but this is optional. Be sure to select a test that is appropriate given the question and decide whether the question calls for a one-tailed or two-tailed test. As well, do not round until the final step of your calculations.

Consider the following propositions: p: You get an A on the final exam. q: You do every exercise assigned in this course. r: You get an A in this class. (a) Translate the statement “You will get an A in this class if you do every exercise assigned in this course or you get an A on the final.” to propositional logic, using p, q, and r. (b) Write the truth table for the statement you wrote in (a). Is the statement a tautology? If not, provide a counter example. (c) What is the negation of the statement you wrote in (a)? (d) Write the truth table for the negation. For what combination(s) of values of p, q, and r is the negation true?

WITHOUT USING MEGASTAT - PLEASE SHOW HOW TO CALCULATE EACH STEP IN EXCEL.

SHOW FULL EQUATIONS

Siders Breakfast Foods Inc., produces a popular brand of raisin bran cereal. The package indicates it contains 25.0 ounces of cereal. To ensure that the firm makes good in its marketing promo claim regarding box weight content, the Siders inspection department makes hourly check on the production process. As part of the hourly check, four boxes are selected and their contents weighed. The results for 25 samples are reported below.

1. Develop the appropriate control charts to evaluate and monitor the boxing process (10 pts)
2. What do the control charts tell you about the process during the 25-hour inspection period (i.e. Do a thorough interpretation and analysis of the charts.)? (10 pts)

3. An FDA regulation controlling the contents of packaged food items states that no more than 5 percent of the items produced and sold can contain less than 95 percent of the stated/labeled weight. Assuming that the standard deviation of the process, when in control or is operating as expected, is 0.90, determine if Siders Breakfast Foods, Inc., is in compliance or not in compliance with the FDA regulation given these parameters, i.e. process mean of 25 ounces and standard deviation of 0.90. Explain and show evidence supporting your conclusion. (10 pts). What should Siders Breakfast do if they discover their process to be in violation of the Federal regulation? (5 pts)

   (Assume that the content weight follows the normal distribution).

A report from the U.S. Department of Agriculture shows that the mean American consumption of carbonated beverages per year is greater than 52 gallons. A random sample of 30 Americans yielded a sample mean of 69 gallons. Assume that the population standard deviation is 20 gallons, and the consumption of carbonated beverages per year follows a normal distribution. Calculate a 95% confidence interval, and write it in a complete sentence related to the scenario.

a) Suppose each of the following confidence intervals were calculated using the same sample. Circle the interval that is at the lower confidence level. State the sample proportion that was used to construct these intervals. (.25, .35), (.24, .36)

b) Suppose you want a confidence interval to be more narrow. What two things can you do to achieve this?

c) For a given sample, which would you prefer, a wider interval or a more narrow one? Why?

d) Suppose your sample proportion is 0.17, with n = 100. How many “successes” were in your sample?

e) Suppose you have a sample with n = 27. Nine of your sample values are found to have the characteristic of interest. Are the 4 conditions required to do a confidence interval met?

f) True or False: a 95% confidence interval for p always contains p.