If x is a binomial random variable, compute p(x) for each of the following cases:

(a) n=3,x=2,p=0.9 p(x)=

(b) n=6,x=5,p=0.5 p(x)=

(c) n=3,x=3,p=0.2 p(x)=

(d) n=3,x=0,p=0.7 p(x)=

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 76.3 with a standard deviation of 5.6. A random sample of 17 supermarkets from Region 2 had a mean sales of 86.5 with a standard deviation of 6.8. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.1 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 4 : State the null and alternative hypotheses for the test. Step 2 of 4 : find the value test statistic Step 3 of 4 : determine the decision rule for the null hypothesis. round to 3 decimal places. Step 4 of 4 : state the tests conclusion

A batch of 400 sewing machines contains 6 that are defective.

(a) Three sewing machines are selected at random, without replacement. What is the probability that the second sewing machine is defective, but the first and third are acceptable?

(b) Three sewing machines are selected at random, without replacement. What is the probability that the third sewing machine is defective, given that the first two are acceptable?

(c) Sewing machines are selected, this time with replacement. What is the probability that the tenth machine selected is the first defective one?

(d) Sewing machines are selected, with replacement. What is the expected number of machines selected until you find two defective ones?

Constructing Confidence Intervals In Exercises 17 and 18, you are given the sample mean and the sample standard deviation. Assume the variable is normally distributed and use a normal distribution or a t-distribution to construct a 90% confidence interval for the population mean u. If convenient, use technology to construct the confidence intervals.

(a) In a random sample of 10 adults from the United States, the mean waste generated per person per day was 4.54 pounds and the standard deviation was 1.21 pounds. (b) Repeat part (a), assuming the same statistics came from a sample size of 500. Compare the results. (Adapted from U.S. Environmental Protection Agency)

answer

a

b

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer calculating miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at fill-up. The driver wants to determine if these calculations are different.

(b) Carry out the test. (Round your answer for t to four decimal places.)
t =?

(c) Give the degrees of freedom.

(d) Give the P-value. (Round your answer to four decimal places.)

2. A least squares adjustment is computed twice on a data set. When the data is minimally constrained with 10 degrees of freedom, a variance of 1.07 is obtained. In the second run, the fully constrained network has 13 degrees of freedom with a variance of 1.56. The a priori

estimate for the reference variances in both adjustments are one; that is,

(1) What is the 95% confidence interval for the reference variance in the minimally constrained adjustment? The population variance is one. Does this interval contain one?

(2) What is the 95% confidence interval for the ratio of the two variances? Is there reason to be concerned about the consistency of the control? Statistically justify your response.

1. Given the incidence matrix shown below: a. Apply the ranking order clustering algorithm in order to establish the appropriate part families and machine cells (20 points). 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 b. Based on your clustering outcome above, how many cells will you use and what machines/processes and parts will be utilized in each cell? Are there any inefficiencies in your design? If so, describe them and how you might make improvements (10 points).  

An experiment was conducted see the effect on fertilizer on production of Mameys. H0 : fertilizers have no impact on mamey production. H1 : fertilizers have an impact on mamey production. There are four treatment (a=4); three types of fertilizer and the control. Each treatment has four replicates (n=4). The number of mameys produced is given in the table below.

A. Using these data complete a 1-Way ANOVA table.

F1: 1, 2, 6, 11

F2: 2, 4, 2, 4

F3: 12, 4, 2, 6

Con: 3, 3, 1, 1

B. What is the proportion of explained variance for this treatment?

Plotted on the horizontal axis is distance in miles to different cities, the vertical axis is price of flight of the flight to these cities

a. looking at the scatter plot, how is the cost of the trip associated with the distance of the trip

b. use a straight edge to approximate a line of best fit to the data

c. on a scale of 0 to 1 estimate how well the line fits the data. 0= no fit 1= perfect fit. How did we choose the value of 0 or 1

d. Find the equation based on your best fit line.  HINT:  To find the estimated equation, pick two points on the line and plug into    Show your work.   Write your equation in the form,

e

.Now, let’s calculate the least-squares line based on your data.  Show your work.  You can use the following table to assist you or you may use Excel if you are more comfortable with the software. Write your equation in the form, .

Determine the Sample Correlation Coefficient, .  

A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. The population mean is $25 and the population standard deviation is $15. What is the probability that a sample of $100 steady smokers spend between $24 and $26?

a. 0.495

b. 0.252

c. 0.248

d. 0.748

2.         Complete the following in regard to the footlength and height categories of the data set:                                                                                                     

a.   In the region to the right, produce a scatterplot of the height versus footlength data (remember this means footlength runs along the horizontal axis as the independent variable and height along the vertical axis as the dependent variable.)  Based upon your scatterplot, briefly discuss below your thoughts on whether the “visual” trend between the individuals’ footlength and height appears linear, curvilinear, or has no general trend at all.                                                                                      

b.  Complete the following:                                                                                      

      i.           Include the trend line's graph and equation on the scatterplot created in part a.  Give the line's equation below and explain within this context what the "x" and "y" variables represent in the equation.                                                                                

ii.         Below, explicitly state the slope of your trend line and discuss what the value of the slope signifies in terms of this context.   

c.          Determine the value of the correlation coefficient (r) for this paired data.  Explain what this value tells you regarding these two variables.  Determine the value of the coefficient of determination (r^2) for this paired data.  Explain what this value tells you regarding these two variables.                                                                    

d.         Using the predicition equation from part bi. above, predict the height of an individual whose footlength is 24.5 cm.                                                                   

e.         Finally, critique the statement “since the correlation coefficient is statistically significant then this means that having a long foot causes one to be tall.”  Specifically, address the issue of “causation” in relation to significant statistical correlation.

A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or an agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major. What would be a Type II error?

Saying that the person is an agriculture major when in fact the person is an agriculture major.

Saying that the person is a business major when in fact the person is a business major.

Saying that the person is a business major when in fact the person is an agriculture major.

Saying that the person is an agriculture major when in fact the person is a business major.