Age Group 15-24 25-34 35-44 45-64 years years years years 6. 4 Male 3. Female 3. 3 4 6. Sex

Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 180 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (Each expert I have asked has gotten the critical value wrong so I added a picture of the correct formula to…

The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1079 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample size Groups mean variance Less than h.s. High school Bachelor's 258 40.9 101.8 263 41.8 97.5 270 42.2 94.4 Graduate 288 43.0 98.7 Send data to calculator Send data to Excel To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the following statistic. Variation between the samples F= Variation within the samples For the data from…

The World Bank collects information on the life expectancy of a person in each country ("Life expectancy at," 2013) and the fertility rate per woman in the country ("Fertility rate," 2013). The data for 12 randomly selected countries for the year 2011 are shown in the table below. Table: Data of Fertility Rates versus Life Expectancy   Fertility Rate Life Expectancy 1.7 77 5.8 55 2.2 70 2.1 76 1.8 75 2.0 78 2.6 73 1.5 81 6.9 54 2.9 72 4.7 63 6.8 57 The most commonly used type of correlation is Pearson correlation, named after Karl Pearson, introduced around the turn of the 20th century. Pearson's r measures the linear relationship between two variables, say X and Y. Find the Pearson’s correlation coefficient for the above data In reference to the calculated correlation coefficient above, describe the strength of the correlation. Briefly give an explanation to meaning of the above results. Obtain the…

A random sample of 10 compact cars, 10 mid-size cars, and 10 luxury cars were selected. The time (in seconds) each of the randomly selected cars required to accelerate from 0 to 60 mph was looked up on the Autos.com website. The results are presented below. Car Type Time       (in seconds) Required to Accelerate from 0 to 60 mph Compact                9.3 8.1 10.2 8.8 9.0 9.3 7.7 9.2 9.4 8.6 Mid-Size                6.9 5.7 8.3 7.7 8.6 5.9 6.1 8.8 6.1 7.2 Luxury                   5.7 6.3 5.4 4.7 6.2 7.0 5.9 5.3 6.3 5.0 Conduct a hypothesis test using ! = 0.05 to determine whether the mean time required to accelerate from 0 to 60 mph is the same for compact, mid-size, and luxury cars. (No accounting or excel, I need help solving it.)

The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratiost. 9 20 11 35 19 13 15 21 29 53 16 26 21 14 21 27 10 12 47 14 40 18 60 72 33 14 8 49 5 16 8 19 12 31 67 51 26 18 17 20 19 13 25 23 27 44 20 27 19 18 32 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.) (b) Find a 90% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper limit (c) Find a 99% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper…

Forbes magazine published data on the best small firms in 2012. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporate CEOS for a random sample of these firms. 48 58 51 61 56 59 74 63 53 50 59 60 60 57 46 63 57 55 47 55 57 43 61 62 49 67 55 67 55 49 Use this sample data to construct a 90% confidence interval for the mean age of CEO's for these top small firms. Use the Student's t-distribution (a) what is the lower bound for 90% confidence interval for the mean age of CEO's? (Round to 3decimal places) UESTION 32 (b) What is the upper bound (Round to 3 decimla places)

The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Private Public 52.8 20.3 43.2 22.0 45.0 28.2 33.3 15.6 44.0 24.1 30.6 28.5 45.8 22.8 37.8 25.8 50.5 18.5 42.0 25.6   14.4   21.8 Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.95% confidence interval, private colleges have a population mean annual cost ____ to ____.

Foxbees magazine published data on the best small firms in 2012. These publicly traded firms have a stock price of at least $5 per share and have reported annual revenue between $5 million and $1 billion. The data below shows the ages of the corporate CEOS for a random sample of these firms. 49 67 59 48 45 49 39 44 37 38 48 38 43 48 62 74 70 58 58 40 74 35 36 54 38 45 54 55 64 75 69 36 55 72 69 60 40 64 39 59 74 52 40 49 38 38 74 50 55 50 R vector Copy to clipboard a) What is the mean of the sample? (Round to 4 decimal places) b) What is the standard deviation of the sample mean or the standard error? (Round to 4 decimal places) c) What is the sample size? (Round to whole number)

The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1116 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample Groups size mean variance Less than 281 41.6 115.8 h.s. High school 260 43.3 96.3 Bachelor's 294 42.5 100.5 Graduate 281 44.2 108.2 Send data to Excel Based on these summary statistics, we perform a one-way, independent-samples ANOVA test to determine if there is a difference in the mean hours worked in a typical week among the four populations of workers. (a) The results of this ANOVA are given in the incomplete ANOVA table below. Complete the…