You measure 22 dogs' weights, and find they have a mean weight of 39 ounces. Assume the population standard deviation is 9.8 ounces. Based on this, construct a 99% confidence interval for the true population mean dog weight.

Give your answers as decimals, to two places

±±  ounces

29) After elections were held, it was desired to estimate the proportion of voters who regretted that
they did not vote. How many voters must be sampled in order to estimate the true proportion to
within 2% (e.g., + 0.02) at the 90% confidence level? Assume that we believe this proportion lies
close to 30%.
A) n = 2017
B) n = 1421
C) n = 2401
D) Cannot determine because no estimate of p or q exists in this problem.
E) n = 1692

For the given binomial sample size and null-hypothesized value of p0, determine whether the sample size is large
enough to use the central limit theorem to conduct a test of the null hypothesis Ho: p = p0.
n = 700, p0 = 0.01
A) No
B) Yes

Last year medical students are sent to rural places in order to
medicate and relieve the inhabitants of this population who do not have access to health
quality. An aspiring doctor finds that a quarter of a population
is vaccinated against malaria. In an epidemic of this disease, he observes that
of every 5 patients 1 is vaccinated. It is also known that of every 12 vaccinated only
1 is sick. The doctor wants to calculate the probability that a non-vaccinated person is
sick

The wheat harvesting season in the American Midwest is​ short, and farmers deliver their truckloads of wheat to a giant central storage bin within a 2​-week span. Because of​ this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned​ cooperatively, and it is to every​ farmer's benefit to make the​ unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop​ damage, it is easy to assign a waiting and unloading cost for truck and driver of ​$17 per hour. During the 2​-week harvest​ season, the storage bin is open and operated16 hours per​ day, 7 days per​ week, and can unload 34 trucks per hour according to a negative exponential distribution. Full trucks arrive all day long​ (during the hours the bin is​ open) at a rate of about 30 per​ hour, following a Poisson pattern

​e) The total daily cost to the farmers of having their trucks tied up in the unloading process​ = ____ per day ​(round your response to the nearest whole​ number).

​f) As​ mentioned, the cooperative uses the storage bin heavily only 2 weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50​% next year. It will cost ​$8 comma ____ to do so during the​ off-season. The one-year net​ cost/benefit to enlarge the storage area​ =____ (round your response to the nearest whole​ number).

The file banking.txt attached to this assignment provides data acquired from banking and census records
for different zip codes in the bank’s current market. Such information can be useful in targeting
advertising for new customers or for choosing locations for branch offices. The data show
- median age of the population (AGE)
- median income (INCOME) in $
- average bank balance (BALANCE) in $
- median years of education (EDUCATION)
Use r

Use R to fit a regression model to predict balance from age, education and income. Analyze the
model parameters. Which predictors have a significant effect on balance? Use the t-tests on the
parameters for alpha=.05. [2 pts = 1 pt R code + 1 pt answer]
f) If one of the predictors is not significant, remove it from the model and refit the new regression
model. Write the expression of the fitted regression model. [2 pts = 1 pt R code + 1 pt answer]
g) Interpret the value of the parameters for the variables in the model. [1 pt]
h) Report the value for the R2
coefficient and describe what it indicates. [1 pt]
i) According to census data, the population for a certain zip code area has median age equal to 34.8
years, median education equal to 12.5 years and median income equal to $42,401.
- Use the final model computed in point (f) to compute the predicted average balance for the zip
code area. [1 pt]
- If the observed average balance for the zip code area is $21,572, what’s the model prediction
error? [1 pt]
j) Conduct a global F-test for overall model adequacy. Write down the test hypotheses and test statistic
and discuss conclusions.

Age        Education            Income Balance

35.9        14.8        91033    38517

37.7        13.8        86748    40618

36.8        13.8        72245    35206

35.3        13.2        70639    33434

35.3        13.2        64879    28162

34.8        13.7        75591    36708

39.3        14.4        80615    38766

36.6        13.9        76507    34811

35.7        16.1        107935 41032

40.5        15.1        82557    41742

37.9        14.2        58294    29950

43.1        15.8        88041    51107

37.7        12.9        64597    34936

36           13.1        64894    32387

40.4        16.1        61091    32150

33.8        13.6        76771    37996

36.4        13.5        55609    24672

37.7        12.8        74091    37603

36.2        12.9        53713    26785

39.1        12.7        60262    32576

39.4        16.1        111548 56569

36.1        12.8        48600    26144

35.3        12.7        51419    24558

37.5        12.8        51182    23584

34.4        12.8        60753    26773

33.7        13.8        64601    27877

40.4        13.2        62164    28507

38.9        12.7        46607    27096

34.3        12.7        61446    28018

38.7        12.8        62024    31283

33.4        12.6        54986    24671

35           12.7        48182    25280

38.1        12.7        47388    24890

34.9        12.5        55273    26114

36.1        12.9        53892    27570

32.7        12.6        47923    20826

37.1        12.5        46176    23858

23.5        13.6        33088    20834

38           13.6        53890    26542

33.6        12.7        57390    27396

41.7        13           48439    31054

36.6        14.1        56803    29198

34.9        12.4        52392    24650

36.7        12.8        48631    23610

38.4        12.5        52500    29706

34.8        12.5        42401    21572

33.6        12.7        64792    32677

37           14.1        59842    29347

34.4        12.7        65625    29127

37.2        12.5        54044    27753

35.7        12.6        39707    21345

37.8        12.9        45286    28174

35.6        12.8        37784    19125

35.7        12.4        52284    29763

34.3        12.4        42944    22275

39.8        13.4        46036    27005

36.2        12.3        50357    24076

35.1        12.3        45521    23293

35.6        16.1        30418    16854

40.7        12.7        52500    28867

33.5        12.5        41795    21556

37.5        12.5        66667    31758

37.6        12.9        38596    17939

39.1        12.6        44286    22579

33.1        12.2        37287    19343

36.4        12.9        38184    21534

37.3        12.5        47119    22357

38.7        13.6        44520    25276

36.9        12.7        52838    23077

32.7        12.3        34688    20082

36.1        12.4        31770    15912

39.5        12.8        32994    21145

36.5        12.3        33891    18340

32.9        12.4        37813    19196

29.9        12.3        46528    21798

32.1        12.3        30319    13677

36.1        13.3        36492    20572

35.9        12.4        51818    26242

32.7        12.2        35625    17077

37.2        12.6        36789    20020

38.8        12.3        42750    25385

37.5        13           30412    20463

36.4        12.5        37083    21670

42.4        12.6        31563    15961

19.5        16.1        15395    5956

30.5        12.8        21433    11380

33.2        12.3        31250    18959

36.7        12.5        31344    16100

32.4        12.6        29733    14620

36.5        12.4        41607    22340

33.9        12.1        32813    26405

29.6        12.1        29375    13693

37.5        11.1        34896    20586

34           12.6        20578    14095

28.7        12.1        32574    14393

36.1        12.2        30589    16352

30.6        12.3        26565    17410

22.8        12.3        16590    10436

30.3        12.2        9354       9904

22           12           14115    9071

30.8        11.9        17992    10679

35.1        11           7741       6207

The technology underlying hip replacements has changed as these operations have become more popular (over 250,000 in the United States in 2008). Starting in 2003, highly durable ceramic hips were marketed. Unfortunately, for too many patients the increased durability has been counterbalanced by an increased incidence of squeaking. An article reported that in one study of 146 individuals who received ceramic hips between 2003 and 2005, 13 of the hips developed squeaking.

(a) Calculate a lower confidence bound at the 95% confidence level for the true proportion of such hips that develop squeaking. (Round your answer to three decimal places.)

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 41.5 cases per year. (a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

A)Test for significance of the Coefficient of Determination (F-test using α = 5%)

B) Construct and interpret the confidence interval for the population regression coefficient b₁ (use 1-α = 95%). Data set below and Thanks!

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

(d) Now consider a sample size of 71. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

A statistics practitioner took a random sample of 55 observations from a population whose standard deviation is 35 and computed the sample mean to be 101.

Note: For each confidence interval, enter your answer in the form (Lower limit, Upper limit). You must include the parentheses and the comma between the confidence limits.

A. Estimate the population mean with 95% confidence.

Confidence Interval =

B. Estimate the population mean with 90% confidence.

Confidence Interval =

C. Estimate the population mean with 99% confidence.

Confidence Interval =

When we test H0: μ1 £ μ2, HA: μ1 > μ2 at α = .10, where Picture = 77.4, Picture = 72.2, s1 = 3.3, s2 = 2.1, n1 = 6, and n2 = 6, what is the estimated pooled variance?

A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 840 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student’s t.

(a) Construct an interval estimate of μ with 98% confidence. (Round your answers to 3 decimal places.)
  
The 98% confidence interval is from __to__

(b) Construct an interval estimate of μ with 98% confidence, assuming that s = 30. (Round your answers to 3 decimal places.)
  
The 98% confidence interval is from __to__

(c) Construct an interval estimate of μ with 98% confidence, assuming that s = 60. (Round your answers to 3 decimal places.)
  
The 98% confidence interval is from __to__

(d) Describe how the confidence interval changes as s increases.
  

• The interval stays the same as s increases.

• The interval gets wider as s increases.

• The interval gets narrower as s increases.