US Mail The weights of a certain class of packages which go through the US Mail are normally distributed with a mean value of 22 lbs with a standard deviation of 4 lbs. 1) Referring to US Mail, find the probability that a randomly selected package weighs more than 18 lbs.

a) 0.9332 b) 1.0000 c) 0.0000 d) 0.0668 e) 0.0316

2) Referring to US Mail, find the 65th percentile of package weights, i. e., find a value c so that there is a 65% chance that randomly selected package weighs less than c and there is a 35% chance that a randomly selected box weighs more than c.

a) 12.87 b) 13.28 c) 13.56 d) 13.96 e) 14.28

3) Referring to US Mail, find the probability that a randomly selected package weighs between 4 and 26 lbs.

Several years ago the proportion of Americans aged 18 - 24 who invested in the stock market was 0.20. A random sample of 25 Americans in this age group was recently taken. They were asked whether or not they invested in the stock market. The results follow:

At a .05 level of significance, use Excel to determine whether or not the proportion of Americans 18 - 24 years old that invest in the stock market has changed.

1. You want to know if, on average, households have more cats or dogs. You take an SRS of 8 households and find the data below. # of cats, 2, 0, 3, 2, 0, 4, 0, 2, and the number of dogs is 1, 1, 3, 4, 0, 2, 2, 1. a) determine the populations and parameters being discussed b) determine which tool will be help us find what we need (one sample z test, one sample t test, two sample t test, one sample z interval, two sample t interval) c) Check if the conditions for this tool holds d) Whether or not the conditions hold, use the tool you chose in part (b). Use C=95% for all confidence intervals and a a=5% for all significance test. *be sure that all methods end with a sentence describing the results*

A commonly used practice of airline companies is to sell more tickets than actual seats to a particular flight because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no shows at flight time is 2%. For a particular flight with 380 seats, a total of 384 tickets were sold. Use normal approximation to find the probability that

(a) at most 375 passengers will show up.

(b) the airline overbooked this flight.

(c) between 4 and 8 passengers (both inclusive) will not show up

I just want to check my Answers: for (a) my ans: 0.3821 (b) my ans: 0.0643

If my answers are wrong then please give the correct solution

The following table contains observed frequencies for a sample of 200.  

Test for independence of the row and column variables using  α = .05.  

Compute the value of the  Χ 2 test statistic (to 2 decimals).

The ABC Logistics Company wishes to test a new truck routing algorithm. A random sample of 20 trucks are enrolled in the test. The trucks are randomly assigned to two groups. Trucks in the first group are routed using the current algorithm. Trucks in the second group are routed using the proposed new algorithm. Performance of the algorithm is measured by the number of packages delivered on the test day.

1. Use the P-value approach to test on whether the mean number of packages delivered are the same between the two groups. Assuming the variances are equal between the two groups.

2. Calculate the Cohen’s d.

How do you calculate ANOVA with uneven sets of numbers?

Chicago Families: A survey is taken to estimate the mean annual family income for families living in public housing in Chicago. From a random sample of 30 families, the annual incomes (in hundreds of dollars) are as follows 83 90 77 100 83 64 78 92 73 122 96 60 85 86 108 70 139 56 94 84 111 93 120 70 92 100 124 59 112 79 a) Construct and interpret a 95% confidence interval for b) Construct a 99% confidence interval for u , and compare it with the one from part a.

The data in the accompanying table represent the rate of return of a certain company stock for 11​ months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts ​(a) through ​(d) below.

Month   Rates_of_return_of_the_index_-_x   Rates_of_return_of_the_company_stock_-_y
Apr-07   4.33   3.28
May-07   3.25   5.09
Jun-07   -1.78   0.54
Jul-07   -3.20   2.88
Aug-07   1.29   2.69
Sept-07   3.58   7.41
Oct-07   1.48   -4.83
Nov-07   -4.40   -2.38
Dec-07   -0.86   2.37
Jan-08   -6.12   -4.27
Feb-08   -3.48   -3.77

(a) Treating the rate of return of the index as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

The estimate of β0 is

__?__.

​(Round to four decimal places as​ needed.)

The estimate of β1 is

__?__.

​(Round to four decimal places as​ needed.)

​(b) Assuming the residuals are normally​ distributed, test whether a linear relation exists between the rate of return of the​ index, x, and the rate of return for the company​ stock, y, at the

α=0.10 level of significance. Choose the correct answer below.

State the null and alternative hypotheses.

A.

H0​: β1=0

H1​: β1≠0

B.

H0​: β0=0

H1​: β0>0

C.

H0​: β0=0

H1​: β0≠0

D.

H0​: β1=0

H1​: β1>0

Determine the​ P-value for this hypothesis test.

​P-value=__?__

​(Round to three decimal places as​ needed.)

State the appropriate conclusion at the α=0.10 level of significance. Choose the correct answer below.

A.

Do not reject H0.

There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

B.

Reject H0.

There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

C.

Do not reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.  

D.

Reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.  

​(c) Assuming the residuals are normally​ distributed, construct a​ 90% confidence interval for the slope of the true​ least-squares regression line.

Lower​ bound:

__?__

​(Round to four decimal places as​ needed.)

Upper​ bound:

__?__

​(Round to four decimal places as​ needed.)

​(d) What is the mean rate of return for the company stock if the rate of return of the index is 3.45​%?

The mean rate of return for the company stock if the rate of return of the index is 3.45​% is

__?__​%.

​(Round to three decimal places as​ needed.)

Researchers in a populous country contacted more than​ 25,000 inhabitants aged 25 years to see if they had finished high​ school; 88.5 % of the 12, 499 males and 80.7​% of the 12, 846 females indicated that they had high school diplomas.

​a) What assumptions are necessary to satisfy the conditions necessary for​ inference?

​b) Create a 99​% confidence interval for the difference in graduation rates between males and​ females, p Subscript males Baseline minus p Subscript females.

​c) Interpret your confidence interval.

​d) Is there evidence that boys are more likely than girls to complete high​ school?

1. The researcher from the Annenberg School of Communications is interested in studying the factors that influence how much time people spend talking on their smartphones. She believes that gender might be one factor that influences phone conversation time. She specifically hypothesizes that women and men spend different amounts of time talking on their phones. The researcher conducts a new study and obtains data from a random sample of adults from two groups identified as women and men. She finds that the average daily phone talking time among 15 women in her sample is 42 minutes (with a standard deviation of 6). The average daily minutes spent talking on the phone among 17 men in her sample is 38 (with a standard deviation of 5). She selects a 95% confidence level as appropriate to test the null hypothesis.

a) Please identify the independent variable for the researcher's hypothesis in the text box below.

b) What is the unit of analysis?

c) What is the alpha?

d) State the research and null hypothesis in symbols. Make sure to be as complete as possible (Using H₁: and H₀:).

Prompt:

A friend tells you he only needs a 25% on the final exam to pass his statistics class, and since the exams are always multiple choice with four possible answers he can randomly guess at the answers and still get 25%. Use what you have learned about the binomial distribution to answer the following questions.

Response parameters:

What do you think about your friend’s idea?

Why?

What do you think his chances of getting at least 25% on the exam are?

Do the number of questions on the exam make a difference? If it does, should your friend hope for a 20 question exam or a 100 question exam.

(Tip: it may help if you create a table of Binary probabilities with p = 0.25 and n = number of questions on the exam. Also, don’t confuse the probability of getting exactly 25% of the questions correct and getting at least 25% of the questions correct)

A quick answer is appreciated. Thank you!

The Condé Nast Traveler Gold List provides ratings for the top 20 small cruise ships. The data shown below are the scores each ship received based upon the results from Condé Nast Traveler's Annual Readers' Choice Survey. Each score represents the percentage of respondents who rated a ship as excellent or very good on several criteria, including Shore Excursions and Food/Dining. An overall score was also reported and used to rank the ships. The highest ranked ship, the Seabourn Odyssey, has an overall score of 94.4, the highest component of which is 97.8 for Food/Dining.

(a)

Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions. (Round your numerical values to two decimal places. Let x₁ represent the Shore Excursions score and y represent the overall score.)

ŷ = __________

(b)

Consider the addition of the independent variable Food/Dining. Develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursions and Food/Dining. (Round your numerical values to two decimal places. Let x₁ represent the Shore Excursions score, x₂ represent the Food/Dining score, and y represent the overall score.)

ŷ = ________

(c)

Predict the overall score for a cruise ship with a Shore Excursions score of 80 and a Food/Dining Score of 91. (Round your answer to one decimal place.)

_________

Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 64.1 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 100 words per minute and a standard deviation of 21 words per minute.

a. At what percentile is the child's reading level (round final answer to one decimal place).

b. Create a graph with a normal curve that illustrates the problem.

For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the student's percentile. There is a Normal Distribution Graph generator linked in the resources area. Upload file containing your graph below.

c. Make an argument to the parents of the child for the need for remediation. Structure your essay as follows:

1. A basic explanation of the normal distribution
2. Why the normal distribution might apply to this situation
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. Interpret the answer to part a. including a definition of percentile.
5. Explain how the graph created in part b. represents the child's reading level.
6. Use the answers to parts a. and b. to emphasize the gravity of the situation.
7. Give a suggested course of action.