In each of parts​ (a)-(c), we have given a likely range for the observed value of a sample proportion p. Based on the given​ range, identify the educated guess that should be used for the observed value of p to calculate the required sample size for a prescribed confidence level and margin of error.

a. 0.2 to 0.3

b. 0.1 or less

c. 0.3 or greater

Physical activity of obese young adults. In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject (International Journal of Obesity, Jan. 2007). The study revealed that the overall physical activity of obese young adults has a mean of μ = 320 cpm μ = 320   cpm and a standard deviation of σ = 100 c p m . σ = 100 c p m . (In comparison, the mean for young adults of normal weight is 540 cpm.) In a random sample of n = 100 n = 100 obese young adults, consider the sample mean counts per minute, ¯ x x ‾ . Describe the sampling distribution of ¯ x x ‾ . What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm? What is the probability that the mean overall physical activity level of the sample is greater than 360 cpm?

Please Double Check answers I've recived 3 wrong answers on three diffrent questions today thank you

CNNBC recently reported that the mean annual cost of auto insurance is 1006 dollars. Assume the standard deviation is 245 dollars. You take a simple random sample of 73 auto insurance policies.

Find the probability that a single randomly selected value is less than 973 dollars. P(X < 973) =

Find the probability that a sample of size n = 73 is randomly selected with a mean less than 973 dollars. P(M < 973) =

A sample containing years to maturity and yield for 40 corporate bonds are contained in the data given below.

Years to Maturity		Yield		Years to Maturity		Yield
23.50		4.757		3.75		2.769
21.75		2.473		12.00		6.293
21.50		4.464		17.50		7.411
23.50		4.684		18.00		3.558
27.00		4.799		8.25		0.945
18.25		3.755		23.25		2.966
15.75		7.068		14.75		1.476
2.00		7.043		10.00		1.382
8.75		6.540		23.00		6.334
5.25		7.000		15.25		0.887
11.25		4.823		4.75		4.810
25.75		1.874		18.00		1.238
14.25		5.654		3.00		6.767
19.25		1.745		9.50		3.745
25.00		8.153		17.50		4.186
6.75		6.571		17.00		5.991
23.00		7.506		9.50		7.322
19.00		2.857		5.50		4.871
10.75		8.010		27.50		2.403
21.25		4.214		26.00		4.500

a. What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?

Mean	？ (to 4 decimals)
Standard deviation	？ (to 4 decimals)

b. Develop a 95% confidence interval for the population mean years to maturity. Round the answer to four decimal places.

（ , ） years

c. What is the sample mean yield on corporate bonds and what is the sample standard deviation?

Mean	？(to 4 decimals)
Standard deviation	？(to 4 decimals)

d. Develop a 95% confidence interval for the population mean yield on corporate bonds. Round the answer to four decimal places.

（ , ）percent

As a data scientist of a company, you want to analyze the following data collected by your company which relates the advertising expenditure A in thousands of dollars to total sales S in thousands of dollars. The following table shows this relationship

Advertising Expenditure (A)	Total Sales (S)
18.6	312
18.8	322
18.8	333
18.8	317
19	301
19	320
19.2	305

Using Advertising expenditure (A) as the domain and Total Sales (S) as the range, the data is not a function because the value 18.8 and 19 appear in the domain more than once with a different corresponding value of the range each time.

--Interpret the slope and y-intercept of this equation.

--Express this equation as a function S of A and find its domain.

--Predict the sales if the advertising expenditure is $25000.

A prominent university conducted a survey on the effect of part-time work on student grade point average (GPA). Let x be the hours worked per week and y the GPA for the year. A summary of the results is below. What can the university conclude with an α of 0.05?

n = 21

sigmay = 55

,sigma x = 520

sigmay² = 171

, aigmax² = 15288

sigmayx = 1275

, sigma ( y − ŷ2)  = 24

a) Compute the quantities below.

_Bhat0 =  , Bhat =

What GPA is predicted when a students works 9 hours a week?

b) Compute the appropriate test statistic(s) for H₁: β < 0.

Critical value =  ; Test statistic =

Decision:  

---Select---

Reject H0

Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).

If not appropriate, input and/or select "na" below.

Effect size =  ;  

---Select---

na

trivial effect

small effect

medium effect

large effect

d) Make an interpretation based on the results.

More hours of part-time work significantly predicts a higher GPA.

More hours of part-time work significantly predicts a lower GPA.    

Part-time work does not significantly predict GPA.

Financial analysts know that January credit card charges will generally be much lower than those of the month before. What about the difference between January and the next​ month? Does the trend​ continue? The accompanying data set contains the monthly credit card charges of a random sample of 99 cardholders. Complete parts​ a) through​ e) below.

January	February
902.74	641.04
7212.18	4565.35
4235.42	2270.56
79.92	300.09
4045.57	1377.72
89.29	−120.74
3289.59	1928.85
2419.54	2609.97
83.81	144.83
6.42	392.85
0.00	40.46
564.69	295.63
2712.23	848.62
187.12	162.12
3265.86	2412.45
1523.59	956.31
1359.23	38.03
733.33	2656.79
75.09	64.94
70.29	−70.32
634.53	1862.61
1041.23	478.07
553.08	994.64
1016.27	774.54
1304.94	3368.08
249.39	5.52
48.78	96.93
872.34	890.89
485.94	485.21
616.52	1485.52
1574.18	890.46
422.34	391.43
770.85	323.19
56.53	0.00
1486.78	2253.73
495.28	390.19
1064.88	1065.85
510.65	131.33
5637.68	4942.63
5.49	5.51
871.63	591.44
1636.66	3364.19
92.13	85.99
669.34	1367.13
829.32	280.85
69.24	67.99
830.54	1057.56
2301.44	3317.76
270.67	14.13
210.42	160.52
1012.36	519.35
1044.96	2021.35
298.64	635.44
−29.99	0.00
1634.61	393.34
1731.93	1323.33
0.00	65.16
31.43	28.75
4.95	77.15
1088.69	892.78
26.88	29.03
120.31120.31	32.23
2007.48	815.63
291.31	779.47
104.02	0.00
53.01	66.25
2842.52	1530.91
675.47	293.45
221.86	171.92
37.79	4.78
533.25	880.96
1932.71	1063.55
692.17	915.55
6804.35	5941.41
393.36	466.47
1309.18	302.89
796.21	497.02
0.00	266.64
1040.29	59.45
565.12	206.62
339.14	412.34
5275.34	5324.54
40.09	72.58
43.39	38.45
653.63	480.25
1071.23	416.29
2337.04	1787.19
91.47	175.32
1433.01	1107.78
719.86	307.79
28.61	24.19
980.34	1216.35
1576.18	1810.23
0.00	468.24
161.96	147.68
494.32	1995.28
534.11	935.24
462.45	114.51
1478.23	2093.37

​a) Build a regression model to predict February charges from January charges.

Feb=____+____Jan ​(Round to two decimal places as​ needed.)

Check the conditions for this model. Select all of the true statements related to checking the conditions.

A. All of the conditions are definitely satisfied.

B. The Linearity Condition is not satisfied.

C. The Randomization Condition is not satisfied.

D. The Equal Spread Condition is not satisfied.

E. The Nearly Normal Condition is not satisfied. ​

b) How​ much, on​ average, will cardholders who charged ​$2000 in January charge in​ February? ​$____ ​(Round to the nearest cent as​ needed.)

​c) Give a​ 95% confidence interval for the average February charges of cardholders who charged ​$2000 in January.

($___,$___) ​(Round to the nearest cent as​ needed.) ​

d) From part​ c), give a​ 95% confidence interval for the average decrease in the charges of cardholders who charged ​$2000 in January.

​($___,$___) (Round to the nearest cent as​ needed.)

​e) What​ reservations, if​ any, would a researcher have about the confidence intervals made in parts​ c) and​ d)? Select all that apply.

A. The residuals show increasing​ spread, so the confidence intervals may not be valid.

B. The residuals show a curvilinear​ pattern, so the confidence intervals may not be valid.

C. The data are not​ linear, so the confidence intervals are not valid.

D. The data are not​ independent, so the confidence intervals are not valid.

E. A researcher would not have any reservations. The confidence intervals are valid. Click to select your answer(s).

6) Suppose a multinomial regression model has two continuous explanatory variables ?1 and ?2 ,and they are represented in the model by their linear and interaction terms.
a) For a ? unit increase in ?1, derive the corresponding odds ratio that compares a category ? response to a category 1 response. Show the form of the variance that would be used in a Wald confidence interval.
b) Repeat this problem for a proportional odds regression model.

I. Proof of an assertion regarding a proportion:

1. The municipal government of a city uses two methods to register properties. The first requires the owner to go in person. The second allows registration by mail. A sample of 50 of the method I was taken, and 5 errors were found. In a sample of 75 of method II, 10 errors were found. Test at a significance level of .15 that the personal method produces fewer errors than the mail method.

2. A pharmaceutical firm is testing two components to regulate the pressure. The components were administered to two groups. In group I, 71 of 100 patients managed to control their pressure. In group II, 58 of 90 patients achieved the same. The company wants to prove at a level of significance of .05 that there is no difference in the effectiveness of the two drugs.

Playbill magazine reported that the mean annual household income of its readers is $120,255. (Playbill, January 2006). Assume this estimate of the mean annual household income is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be σ = $33,225.

a. Develop a 90% confidence interval estimate of the population mean.

b. Develop a 95% confidence interval estimate of the population mean.

c. Develop a 99% confidence interval estimate of the population mean.

d. Discuss what happens to the width of the confidence interval as the confidence level is increase. Does this result seem reasonable? Explain.

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 9 hours.

What is the probability that 9 randomly sampled batteries from the population will have a sample mean life of between 70 and 80 ​hours?

According to a recent study annual per capita consumption of milk in the United States is 22.6 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis.

Gallons of Milk
28.3
23.84
25.25
21
17.52
19.61
19.83
26.18
34.97
30.1
28.59
20.57
26.94
27.24

Open spreadsheet

1. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.

   H₀: ? _________> 22.6≥ 22.6= 22.6≤ 22.6< 22.6≠ 22.6

   H_a: ? _________> 22.6≥ 22.6= 22.6≤ 22.6< 22.6≠ 22.6

2. What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?

   (2 decimals) ______

3. At ? = 0.01, test for a significant difference by completing the following.

   Calculate the value of the test statistic (2 decimals).

   _______

   The p-value is  (4 decimals)

4. Reject the null hypothesis?

   _____NoYes

   What is your conclusion?

   _________There is insufficient evidence to conclude that the population mean consumption of milk in Webster City is greater than the hypothesized mean.Conclude the population mean consumption of milk in Webster City is greater than the hypothesized mean.

Let X and Y be independent Exponential random variables with common mean 1.

Their joint pdf is f(x,y) = exp (-x-y) for x > 0 and y > 0 , f(x, y ) = 0 otherwise. (See "Independence" on page 349)

Let U = min(X, Y) and V = max (X, Y).

The joint pdf of U and V is f(u, v) = 2 exp (-u-v) for 0 < u < v < infinity, f(u, v ) = 0 otherwise. WORDS: f(u, v ) is twice f(x, y) above the diagonal in the first quadrant, otherwise f(u, v ) is zero.

(a). Use the "Marginals" formula on page 349 to get the marginal pdf f(u) of U from joint pdf f(u, v) HINT: You should know the answer before you plug into the formula.

(b) Use the "Marginals" formula on page 349 to get the marginal pdf f(v) of V from joint pdf f(u, v) HINT: You found f(v) in a previous HW by finding the CDF of V. You can also figure out the answer by thinking about two independent light bulbs and adding the probabilities of the two ways that V can fall into a tiny interval dv.

(c) Find the conditional pdf of V, given that U = 2. (See page 411). HINT: You can figure out what the answer has to be by thinking about two independent light bulbs and remembering the memoryless property.

(d) Find P( V > 3 | U= 2 ). (See bottom of page 411. Do the appropriate integral, but you should know what the answer will be.)

(e) Find the conditional pdf of U, given that V = 1. (See page 411).

(f) Find P ( U < 0.5 | V = 1).

HINT: You should know ahead of time whether the answer is > or < or = 1/2.

Using the

2 Superscript k Baseline greater than or equals n

​rule, determine the number of classes needed for the following data set sizes.

​a)

nequals

50

​b)

nequals

400

​c)

nequals

1250

​d)

nequals

2500

​a) The number of classes needed when

nequals

50is

nothing

.

​b) The number of classes needed when

nequals

400is

nothing

.

​c) The number of classes needed when

nequals

1250is

nothing

.

​d) The number of classes needed when

nequals

2500is

nothing

.

Question 18

A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:

------------------------------------------------------------

Forecast of demand^a = 1,000 units per week

Forecast error^a, std. dev. =100 units per week

Lead time = 4 weeks

Carrying cost = 25 % per year

Purchase price, delivered = $52 per unit

Replenishment order cost = $20 per order

Stockout cost = $10 per unit

In-stock Probability during the lead time =90%

^a Normally distributed

------------------------------------------------------------

Due to possible rounding effect, please pick the closest number in the following options.

Question 19

If the hospital orders 400 units each time, what’s the total annual costs (holding cost + ordering cost + stock-out cost) excluding purchasing costs?

Question 19 options:

	10000
	21008
	31008
	42016

Use the following information to answer questions 17-20.

A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:

------------------------------------------------------------

Forecast of demand^a = 1,000 units per week

Forecast error^a, std. dev. =100 units per week

Lead time = 4 weeks

Carrying cost = 25 % per year

Purchase price, delivered = $52 per unit

Replenishment order cost = $20 per order

Stockout cost = $10 per unit

In-stock Probability during the lead time =90%

^a Normally distributed

------------------------------------------------------------

Due to possible rounding effect, please pick the closest number in the following options.

Question 20

If the lead time is normally distributed with a mean of 4 weeks and a standard deviation of 0.5 weeks, what’s the reorder point?

Question 20 options:

	4689
	4129
	5188
	6000