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Problems 1.2, 1.17, 3.3 and 3.22

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Problems 1.2, 1.17, 3.3 and 3.22

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You are the manager at a company and are asked to present a report on the year-to-date performance of your division. What type of statistical information would you include in your report? In particular, which descriptive statistics (mean, median, standard deviation, etc.) do you think would best represent the main aspects of the performance of your division? What types of graphical presentation (histogram, dot plot, stem-and-leaf, bar chart, etc.) would you include? Explain your reasoning

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Discuss how the Empirical Rule works and how it relates to the bell curve as illustrated in Figure 3.14 (a). Then, explain Chebyshev’s Theorem and how it is different from the Empirical Rule. Give a specific example of a population with which the Empirical Rule might be most effective and one with which Chebyshev’s Theorem might be most effective. Respond to at least two of your classmates’ postings.

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1.Question : The two types of quantitative variables are

2.Question : As a general rule, when creating a stem-and-leaf display, there should be between ______ stem values.

3.Question : The median is the value below which and above which approximately 50 percent of the measurements lie.

4.Question : Temperature in degrees Fahrenheit is an example of a ____ variable.

5.Question : Stem-and-leaf displays and dot plots are useful for detecting

6.Question : Any characteristic of a population unit is called a

7.Question : The science of using a sample to make generalizations about the important aspects of a population is known as

8.Question : A normal population has 99.73 percent of the population measurements within ___ standard deviations of the mean.

9.Question : When we are choosing a random sample and we do not place chosen units back into the population, we are

10.Question : An example of manipulation of graphical display used to distort reality is:

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Problems 4.4, 4.20, 5.12, 6.22

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**R**elative Frequency. Conceptually we would expect the probability of newborn males and females to be the same. However, census reports indicate that the ratios of males and females in various countries do not conform to the theoretical prediction. What do you think accounts for this variation? Can you think of other cases where the expected probabilities do not quite agree with the empirical values?

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Applications for Probability. In what situations might you use probability as a manager to approach business-related problems? What are the advantages to using probability concepts in business decisions? Are there any disadvantages or possible pitfalls to avoid in using probability in business?

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1.Question : In a statistical study, the random variable X = 1, if the house is colonial, and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous.

2.Question : The set of all possible experimental outcomes is called a(n)

3.Question : If two events are independent, then the probability of their intersection is represented by:

4.Question : A(n) __________ is a measure of the chance that an uncertain event will occur.

5.Question : The price-to-earning ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a Z value equal to 1

6.Question : The expected value of a discrete random variable is:

7.Question : For a continuous distribution, P(a = X = b) = P(a <X< b).

8.Question : The following formula: P(A U B) = P(A) + P(B) – P(A n B) represents

9.Question : The MPG (mileage per gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be less than 33.2?

10. Question : The height of a continuous probability curve over a given point is

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Problems 7.11, 7.30, 8.8, 8.38

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**U**nscientific Sampling. Consider question 7.45 from the text: A Milwaukee television station, WITI-TV, conducted a telephone call-in survey asking whether viewers liked the new newspaper, the Journal Sentinel. On April 26, 1995, Tim Cuprisin, a columnist for the Journal Sentinel, wrote the following comment: “WITI-TV (Channel 6) did one of those polls—which they admit are unscientific—last week and found that 388 viewers like the new Journal Sentinel and 2,629 didn’t like it. We did our own unscientific poll on whether those Channel 6 surveys accurately reflect public opinion. The results: a full 100 percent of the respondents say absolutely, positively not.”

Is Cuprisin’s comment justified?

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Many articles present statistical data and list margins of error (for example, reports on political opinion polls, growth or decline of the housing markets, manufacturing sectors, etc.). Find one such article from a reliable source (such as EBSCO or Proquest) in the online library that includes a construction of confidence intervals for the data studied, and give a summary of the topic and the statistical results presented. In particular, discuss whether there is enough information presented in the article to arrive at the same conclusion as reported

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1.Question : There is little difference between the values of ta/2 and Za/2 when the sample

2.Question : If the population proportion is .4 with a sample size of 20, then is this sample large enough so that the sampling distribution of is a normal distribution.

3.Question : For non-normal populations, as the sample size (n) _________, the distribution of sample means approaches a/an __________ distribution.

4.Question : As the sample size ________the variation of the sampling distribution of ___________.

5.Question : Assuming the same value of a, as the sample size increases, the value of ta/2 approaches the value of Za/2.

6.Question : If the sampled population has mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of for n = 16 are

7.Question : The sampling distribution of x bar must be a normal distribution with a mean 0 and standard deviation 1.

8.Question : As our sample standard deviation increases when all other parts of the confidence interval stay the same, then the confidence interval will become:

9.Question : When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean, µ will be _____ the 95% confidence interval for µ.

10. Question : A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs and 24 lbs respectively, then, based on a sample size of 36 boxes, the probability that the average weight of the boxes will be less than 84 lbs is

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Problems 9.13, 9.22, 12.10, 12.18(a)

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Give an example of a hypothesis test you could perform at work or at home. State what the Null and the Alternative hypotheses would be in your test. Explain how you would settle on a reasonable level of significance for your scenario. Also explain what the type I and II errors would be if you reached the incorrect conclusion in your test.

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Creating Hypotheses. Assume you are the manager of a paint manufacturing factory. Your company has received complaints from customers that the containers hold less than the amount printed on them. On the other hand, corporate management is concerned that the containers hold more than the standard amount. You assign a statistician to verify these claims. A sample of containers was selected and the volume of paint in each container was measured. Assuming that the volume printed on each container is 1 gallon, how would you formulate the null and alternative hypotheses to test the customers’ claim? As a manager, what reasonable criteria will you use to set a value for the level of significance to be used in the test? After answering this question, what type of error would you suppose may result in that case?

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1.Question : Consider using p-value to test H0 versus Ha by setting a equal to .10. We reject H0 at level a of significance if and only if the p-value is:

2.Question : When carrying out a sample test (with ó known) of H0: µ = 10 vs. Ha: µ > 10 by using a rejection point, we reject Ho at level of significance a if and only if the calculated test statistic is

3.Question : When using the chi-square goodness of fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis.

4.Question : The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.

5.Question : For a hypothesis test about a population mean or proportion, if the level of significance is less than the p-value, the null hypothesis is rejected.

6.Question : When we carry out a chi-square test for independence, the null hypothesis states that the two relevant classifications

7.Question : The manager of the quality department for a tire manufacturing company wants to study the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated Z test Statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .10, the null hypothesis would be rejected.

8.Question : A type II error is failing to reject a false null hypothesis.

9.Question : For the chi-square goodness of fit test, the rejection point X2a is in

10.Question : If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .01.

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Linear Correlation. Do you think there is a correlation between CEO salaries and the degree of success of a company? If you were to take a sample of companies with comparable size, market capitalization, and product category, and plot CEO salaries against the net profit of their respective companies, do you expect to find a linear correlation between the two? Explain.

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Visit the websites on Quality Control (QC) listed in the Required Websites for this week. In addition, locate an article on the Internet or in the Library databases that describes an example of the use of statistics in Quality Control. In your post, briefly define Quality Control and explain its importance. Also, describe some of the most widely used tools in the industry for measuring and controlling quality, emphasizing their relationship to what you have encountered in this class. Finally, explain the example from your article of statistics as applied in a Quality Control context.

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1.Calculate the mean yearly value using the average gas prices by month found in the”Final Project Data Set”.

2.Using the years as your x-axis and the annual mean as your y-axis, create a scatterplotand a linear regression line.

3.Answer the following questions using your scatterplot and linear regression line:

- What is the slope of the linear regression line?
- What is the Y-intercept of the linear regression line?
- What is the equation of the linear regression line, in slope-intercept form?* Based on the linear regression line,
- what would be an estimated cost of gas in the year2020?
- What are the residuals of each year?
- Select a current price that you have seen or paid recently for gas. Is that price within therange of the linear regression line or is it an outlier?
- Is it within the confidence interval of5% or either end?

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Imagine that you are a manager at a delivery service and you are creating a report toproject the effects on your company of rising gas prices in the next ten years.

Using thepreceding statistical analysis as your basis and outside scholarly resources to support yourclaims,

Write a 3 to 5 page paper interpreting the results from this perspective. Include thefollowing considerations:

1. Introduce the project and its significance to the company.

2. Explain the statistical analysis that you completed in Part I. Be sure to explain wherethe data came from, what analysis was done, and what the results were.

3. Give conclusions that you have drawn from the data. Consider the effects of your gasprice predictions on the delivery business. Also consider whether or not you believe yourpredicted gas prices are accurate. What could occur in the future that would change yourlinear regression line and therefore your prediction?

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