For each of the questions below, a histogram is described. Indicate in each case whether, in view of the Central Limit Theorem, you can be confident that the histogram would look like approximately a bell-shaped (normal) curve, and give a brief explanation why (one sentence is probably sufficient).

1. The price of one gallon of gasoline at a particular gas station is recorded every day of the year, and the 365 values are plotted in a histogram.

2. Two hundred students in a statistics class each flip a coin 40 times and record the number of heads. The numbers of heads are plotted in a histogram.

3. Two hundred students in a statistics each roll a die 60 times and record the sum of the numbers they got on the 60 rolls. They make a histogram of the 200 sums.

4. One thousand randomly chosen people report their annual salaries, and these salaries are plotted in a histogram.

5. The day before an election, fifty different polling organizations each sample 2000 people and record the percentage who say they will vote for the Democratic candidate. The 50 values are plotted in a histogram.

6. The fifty polling organizations also record the average age of the 2000 people in their sample, and the 50 averages are plotted in a histogram.

7. One hundred batteries are tested, and the lifetimes of the batteries are plotted in a histogram.

We must show our work

6. Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 90 randomly sampled television viewers, 18 indicated that they asked their physician about using a prescription drug they saw advertised on TV. Develop a 90% confidence interval for the proportion of viewers who discussed a drug seen on TV with their physician. (Hint: Review section Confidence Interval for a Population Proportion)

theme park owner wants to know if the children’s rides are favoring 10 year old girls over 10 year old boys based on height. In other words, does one group taller than the other and thus can go on more rides?

Part a: The owner gathered height data on 10 year old girls and 10 year old boys, see data below. Determine at the 5% significance level if there is evidence that the two genders are not the same height and thus cannot all go on the same rides. Show your work and give your answer in complete sentences in context of the problem.

Part b: After doing some research, the owner found the following information about the expected height and standard deviation for 10 year olds. Does that change the result of part a? Show your work and give your answer in complete sentences in context of the problem.

. A business researcher wants to estimate the average number of years of experience an account manager has working with the company before getting promoted to account manager. Eight account managers are randomly selected and asked how long they worked with the company before becoming an account manager. The resulting answers were:     1.2, 4.0, 3.6, 0.7, 5.8, 3.3, 2.8, 4.1

      Use Excel and these data to compute a 90% confidence interval to estimate the average length of time an account manager spent working for the company before they were promoted to account manager. Print out your answer.

      Directions:

For most current versions of Excel, go to the Data tab, select Data Analysis, and Descriptive Statistics. Enter the input range. Check off that you want Summary Statistics and Confidence Interval for the mean. Enter the value of the level of confidence. In the output you will get several things. The value of the mean is the point estimate. The value labeled “confidence level” is actually the + error of the interval. The “error of the interval” already has the table value of t and the standard error of the mean computed within it. Use the mean and the “error of the interval” to make the confidence interval. You will probably have to manually type this out somewhere on the spreadsheet or cut and paste it together in Excel and printout the confidence interval.

uestion 5 (1 point) If μ=5.06 and σ=1.27, find the z-score for x=6.87. Question 5 options: 1.43 2.89 -1.43 -2.89

Question 6 (1 point) If μ=63.81 and σ=7.94, find the z-score for x=50.16. Question 6 options: -1.72 -1.719 1.72 1.719

Question 7 (1 point) Use the following set of sample values to answer the question. 33 36 27 30 35 25 19 23 36 10 20 23 13 21 16 37 26 37 12 32

What is the IQR (interquartile range)? Question 7 options: 14.5 19.5 34 53.5 Question 8 (1 point) Saved Use the following set of sample values to answer the question. 31 23 28 27 19 18 22 19 30 17 13 21 37 10 12 20 13 33 24 26 What is the value of Q3? Question 8 options: 10 45 17.5 27.5

When is the Bayes' rule (not the Bayes' theorem) optimal? Explain the meaning of that by using a
2x2 confusion matrix

2.) Solve this question by hand:

Develop a regression model to predict selling price based on the square footage. Find the value of beta(regression coefficient), coefficient of determination. Test for the significance of the model at 5% level. You must report the test statistic, it's corresponding significance value and the critical value that corresponds to 5%. (You can find a table of the relevant distribution by a google search)

Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 243 with 27.2% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

FCAT scores and poverty. In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam, called the Florida Comprehensive Assessment Test (FCAT). An analysis of the link between FCAT scores and sociodemographic factors was published in the Journal of Educational and Behavioral Statistics (Spring 2004). Data on average math and reading FCAT scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 Florida elementary schools are summarized by the number given below. (x= percentage of students below poverty level, and y=math score ) n = 22 ??xi = 1292.7 ??yi = 3781.1 ??x2i =88668 ??yi2 =651612 ??xiyi =218292 (a) Propose a straight-line model relating math-score to percentage of students below poverty level. (b) Find the least-squares regression line fitting the model to the data. (c) Interpret the estimates for intercept and slope in the context of the problem. (d) Test whether the math score is negatively related to the percentage of students below the poverty level. (e) Construct a 99% confidence interval for the slope of the model, and interpret your result in the context of the problem.

Leisure Air, a regional airline, provides service for Pittsburgh, Newark, Charlotte, Myrtle Beach, and Orlando. Leisure Air has two Boeing 737-400 airplanes, one based in Pittsburgh and the other in Newark. Both airplanes have a coach section with a 132-seat capacity. Each morning the Pittsburgh-based plane flies to Orlando with a stopover in Charlotte, and the Newark-based plane flies to Myrtle Beach, also with a stopover in Charlotte. At the end of the day, both planes return to their home bases. We restrict our attention to the Pittsburgh-Charlotte, Charlotte-Orlando, Newark-Charlotte, and Charlotte-Myrtle Beach flight legs for the morning flights.

Leisure Air uses two fare classes: a discount-fare Q class and a full-fare Y class. Reservations using the discount-fare Q class must be made 14 days in advance and must include a Saturday night stay in the destination city. Reservations using the full-fare Y class may be made any time, with no penalty for changing the reservation at a later date. Leisure Air established fares and developed forecasts of customer demand for each of 16 ODIFs. These data are shown in the table below.

But because demand cannot be forecasted perfectly, the number of seats actually sold for each origin-destinationitinerary fare (ODIF) may turn out to be smaller or larger than forecasted. Suppose that Leisure Air believes that economic conditions have improved and that its original forecast may be too low. To account for this possibility, Leisure Air is considering switching the Boeing 737-400 airplanes that are based in Pittsburgh and Newark with Boeing 757-200 airplanes that Leisure Air has available in other markets. The Boeing 757-200 airplane has a seating capacity of 158 in the coach section.

a.    Because of scheduling conflicts in other markets, suppose that Leisure Air is only able to obtain one Boeing 757-200. Should the larger plane be based in Pittsburgh or in Newark?

Newark

Explain.

The total revenue of basing the larger plane in Newark is bigger than basing the larger plane in Pittsburgh.

b.    Based upon your answer in part (a), determine a new allocation for the ODIFs.

Original allocation:

c.   
Using a larger plane based in Newark, the optimal allocations are:

d.   
Briefly summarize the major differences between the new allocation using one Boeing 757-200 and the original allocation summarized above.

The main differences between the original allocations and the new allocations are in the variables:

CMQ, COQ, PMQ, NMQ, and POQ

e.    Suppose that two Boeing 757-200 airplanes are available. Determine a new allocation for the ODIF’s using the two larger airplanes. Using a larger plane based in Pittsburgh and a larger plane based in Newark, the optimal allocations are:

f.    
Briefly summarize the major differences between the new allocation using two Boeing 757-200 airplanes and the original allocation shown in part (b).

The main differences between the allocations in part b and the new allocations are in the variables:

CMQ, COQ, NMQ, and POQ

This solution provides an increase in revenue of $  .

g.    Consider the new solution obtained in part (b). Which ODIF has the highest bid price?

COY

What is the interpretation for this bid price?

The bid price for this solution is $   which means that if there was one more Y class seat revenue would increase by $  .

The average annual rainfall in City A is 20 inches, with a standard deviation of 3 inches. The annual rainfall in City B is 45 inches, with a standard deviation of 12 inches. In a given year, City A received 25 inches, while City B received 55 inches. Assuming both rainfall distributions are approximately normal, which city had the wettest year relative to its average distribution?

a.City A

b.City B

c.The cities had equally wet years

d.Cannot tell from the information given

Sampling and Sample Distribution and Errors: during those times it is difficult to count an entire population, sampling is one great way to test that population and the results. These are results that a statistic can take and how often each result can happen. The textbook in Chapter 7 discusses the Cell Phone Case Cost reduction by companies as one example. Briefly discuss the importance to a company when it comes to sampling. Terms like mean and standard deviation and sample errors should be factored into your discussion. Try to incorporate a real example outside the textbook examples.

Ads: A company is willing to renew it advertising contact with a local radio station only if the station can prove that more than 20% of the residents of the city heard the ad and not recognize the company’s product. The radio station conducts a random phone survey of 400 people.

A) What are the hypotheses

B) The station plans to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%?

C) What is meant by the power of the test?

D) For which level of significance will the power of the test be higher? Why?

E) They finally agree to use a = 0.05, but the company proposes that the station call 600 people instead of the 400 initially proposed. With that make the risk of Type II error higher or lower? Explain

A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 70 thousand miles and a standard deviation of 12 thousand miles. Complete parts​ (a) through​ (c) below.

a. What proportion of trucks can be expected to travel between 53 and 70 thousand miles in a​ year? (Round to four decimal places as​ needed.)