Question 4 [25]
The Zambezi car battery manufacturer claims that the average lifespan of batteries produced by his firm is at least 30 months. The rival manufacture the Rehoboth batteries disagree and took random sample of 100 Zambezi car batteries and recorded a mean of 31.7 months and a standard deviation of 8 months. (Show all your works)
Determine the following:
a) The null and alternative hypotheses

b) The test statistic value.

c) The critical statistics value at 99% confidence level

d) The rejection region using critical value approach

e) The p value at 99% confidence level

f) The rejection region using both the p value approach

g) Make conclusion about the population mean using both approaches

Victoria’s Secret online offers 2,500 items for sale, 60 of them are offered to VIP’s only. Fredricks of Hollywood offers 1,300 items, where 45 are available to VIP members only. I believe that the proportion of VIP only items on the Fredricks website is more than the proportion of VIP items on the VS website.

Gather appropriate data and post the solution to compare these two proportions.

Find the critical value from the Studentized range distribution for H0: μ1 = μ2 = μ3 = μ4 = μ5, with n = 35 at α = 0.01. Round to the nearest 3 decimal places.

Question 3 [25]
OK furniture store submit weekly records the number of customer contacts contacted per week. A sample of 50 weekly reports showed a sample mean of 25 customer contacts per week. The sample standard deviation was 5.2. (Show all your works)
a) Compute the Margin of error at 0.05 significant level

b) Provide a 95% confidence interval for the population mean.

c) Compute the Margin of error at 0.01 significant level

d) Provide a 99% confidence interval for the population mean.

e) With a 0.99 probability, what size of sample should be taken if the desired margin of error is 1.5

Two nonprofits are interested in sharing fundraising lists and campaigns as they think their donors share common interests. Implicit in that assumption is they are related variables. You collect data below for thirteen donors and want to test if there is a relationship between donations (in dollars) (data is collected below)

Charity A:  

50 70 60 30 30 60 100 20 40 60 30 80 60

Charity B:

60 45 65 50 30 30 90 40 50 70 40 55 40

a.) State the null both formally and in lay terms
b) Calculate r and the regression line (y = a + bx) and reject/accept at a=.05. What is the regression line please state it?

c) Explain your findings in lay terms using r-square, r, b as appropriate

d) Calculate a 95% confidence interval for the slope if it is necessary if it is not please explain. Provide the formal interval and explain in layterms.

A. For a series of 1500 tosses, what is the natural logarithm of the total number of microstates associated with 50% heads and 50% tails? (Note: Stirling’s approximation will be useful in performing these calculations).

B. How much less probable is the outcome that the coin will land 40% heads and 60% tails? (Note: Stirling’s approximation will be useful in performing these calculations).

nfatal disease akin to leprosy. This test can identify patients before the onset of symptoms in order to begin early treatment. The group tested 50,000 people across different villages from the Stormlands and recorded their findings in the table below. The presence of the disease was validated by later onset of symptoms. Disease Present Disease Not Present Tested Positive 54 36 Tested Negative 9 49,901 Calculate the following, showing all calculations: 1) Disease Prevalence 2) Sensitivity 3) Specificity 4) Positive Predictive Value 5) Negative Predictive Value Would you consider this a good diagnostic test? Justify your answer.

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.)

s = lb

(b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

Suppose you gather the following test scores from you fellow students: 92,71,67,81,73,90,76,76,85,77,62,99.
A.The upper quartile is 85
B.The interquartile range is 15.5
C.The lower quartile is 71
D.The median quartile is 76

Respond to the following in a minimum of 175 words, please type response:

The standard error of the estimate of the mean is represented by the equation: σ√n Discuss what this equation means, using your own words and explain why we use it. Consider how it relates to the fact that we are making assumptions about the population and not just the sample.

1a.) If a constant c is added to each xi in a sample, yielding yi = xi + c, how do the sample mean and median of the yis relate to the mean and median of the xis? Verify your conjectures. Verify using a made-up example.

1b.) If each xi is multiplied by a constant c, yielding yi=cxi, answer the question of part (a). Again, verify your conjectures. Verify using a made-up example.

PLEASE SHOW HOW TO CALCULATE EACH STEP IN EXCEL.

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).

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Steams /              Leaves

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

(b) What is a typical, or representative, flow rate?

L/min

(c) Does the display appear to be highly concentrated or spread out?

spread out.

highly concentrated in the middle.

highly concentrated, except for a few values on the positive side.

highly concentrated, except for a few values on the negative side.

(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?

Yes, the distribution appears to be reasonably symmetric.

No, the data are skewed to the right, or positively skewed.

No, the data are skewed to the left, or negatively skewed.

No, the distribution of the values appears to be bimodal.

(e) Would you describe any observation as being far from the rest of the data (an outlier)?

Yes, the value 2.1 appears to be an outlier.

Yes, the value 15.5 appears to be an outlier.

Yes, the value 18.4 appears to be an outlier.

No, none of the observations appear to be an outlier.

35. The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service. For this group, 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012). Suppose 10 firstround appeals have just been received by a Medicare appeals office.

PLEASE SHOW HOW TO COMPUTE ANSWERS IN EXCEL USING EXCEL FORMULAS

a. Compute the probability that none of the appeals will be successful.

b. Compute the probability that exactly one of the appeals will be successful.

c. What is the probability that at least two of the appeals will be successful?

d. What is the probability that more than half of the appeals will be successful?