Q2. According to a PNC Financial Independence Survey released in March 2012, today's U.S. adults in their 20s “hold an average debt of about $45,000, which includes everything from cars to credit cards to student loans to mortgages" (USA TODAY, April 24, 2012). Suppose that the current distribution of debts of all U.S. adults in their 20s has a mean of $45,000 and a standard deviation of $12,720. Find the probability that the average debt of a random sample of 144 U.S. adults in their 20s is a. less than $42,600 b. more than $46,240
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- Based on research conducted by the government on people aged 25 to 34 years, on average, people in that age group spend $1,994 of their annual income on entertainment. Assume that the data are normally distributed with a standard deviation of $450. What percentage of the population in this age group spends less than $1,000 per year for entertainment?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 ratios†. 11 35 19 13 15 21 40 18 60 72 9 20 29 53 16 26 21 14 21 27 10 12 47 14 33 14 18 17 20 19 13 25 23 27 5 16 8 49 44 20 27 8 19 12 31 67 51 26 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 four decimal places.) x = s = (b) Find a 90% confidence interval for the P/E population mean ? 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 ? of all large U.S.…According to the U.S. Census Bureau, the average household income was $73,298 in 2014 (the latest year for which complete data is available). The median household income in 2014 was $53,719. Does a $20,000 difference seem like a big deal in these two different measures? What explains the discrepancy? Which measure do you think better captures the central tendency (or lay person’s sense of “average”) of the distribution of income in this country?
- 3. The foreign service exam gives passing grade to only the top 10% of those taking the exam. The mean score is 84, with a standard deviation of 8. What should be the minimum passing grade?A polling organization reported data from a survey of 2000 randomly selected Canadians who carry debit cards. Participants in this survey were asked what they considered the minimum purchase amount for which it would be acceptable to use a debit card. Suppose that the sample mean and standard deviation were $9.14 and $7.70, respectively. (These values are consistent with a histogram of the sample data that appears in the report.)Do these data provide convincing evidence that the mean minimum purchase amount for which Canadians consider the use of a debit card to be appropriate is less than $10? Carry out a hypothesis test with a significance level of 0.01. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = State your conclusion. Reject H0. We do not have convincing evidence that the mean minimum purchase amount for which Canadians consider it…4) The table shows, for the years 1997–2012, the mean hourly wage for residents of the town of Pity Me and the mean weekly rent paid by the residents. Mean hourly wage (dollars) Mean hour. Mean weekly rent (dollars) Mean weekly rent (dollars) Year Year (dollar 116 1997 57 10.38 2005 28.99 59 113 1998 10.89 2006 28.63 2007 1999 62 11.96 112 36.75 14.55 2000 63 12.46 2008 86 17.90 2001 86 17.72 2009 90 2002 2010 119 28.07 90 14.67 131 35.24 2003 2011 17.97 100 122 2004 2012 22.23 31.87 115 Find the least squares line that uses mean hourly wage to predict mean weekly rent. Round values to the nearest ten-thousandth. Include a scatter plot with the regression lino
- A dataset from 1987 contains information about credit card applications and approvals for 690 applicants. We are interested in looking at the amount of debt across industries, specifically between information technology, healthcare, real estate, and education. The following values are scaled down for ease of analysis. From the sample, 45 are in information technology with an average of $4.03 dollars in debt and a standard deviation of $3.88. 52 are in the healthcare industry with an average of $5.84 dollars in debt and a standard deviation of $6.58. 30 are in real estate with an average of $4.79 dollars in debt and a standard deviation of $5.43. 30 are in education with an average of $8.21 dollars in debt and a standard deviation of $6.25. Fill in the hypotheses below: Ho: All the means are equal. Ha: At least one mean is different from the others. ✓ Part 2 of 3 Complete the following ANOVA summary table (a = 0.01). Round your answers to three decimal places, if necessary, and round…2b) Find the mean and the standard deviation of the times in the following table. Because the table contains all the winning times for this race (up to year 2012), the data set is a population. Olympic Women's 400-Meter Dash Results, in Seconds, 1969-2012 52.0 51.08 49.29 48.88 48.83 48.65 48.83 48.25 49.11 49.41 49.62 49.55
- An article in the San Jose Mercury News stated that students in the California state universitysystem take 4.25 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 64 students and obtain a sample mean of 4.5 with a sample standard deviation of 1.5. Do the data support your claim at the 1% level?A dataset from 1987 contains information about credit card applications and approvals for 690 applicants. We are interested in looking at the amount of debt across industries, specifically between information technology, healthcare, real estate, and education. The following values are scaled down for ease of analysis. From the sample, 44 are in information technology with an average of $4.03 dollars in debt and a standard deviation of $3.88. 55 are in the healthcare industry with an average of $5.84 dollars in debt and a standard deviation of $6.58. 33 are in real estate with an average of $4.79 dollars in debt and a standard deviation of $5.43. 20 are in education with an average of $8.21 dollars in debt and a standard deviation of $6.25. Fill in the hypotheses below: Ho: Select an answer Ha: Select an answerThe National Assessment of Educational Progress (NAEP) is a nationwide assessment of students' proficiency in nine subjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The main NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12. Suppose in 2000, the science scores for female students had a mean of 146 with a standard deviation of 35. Assume that these scores are normally distributed with the given mean and standard deviation. The normal curve representing this distribution of the scores is symmetrical about a vertical line through . The value 41 is below the mean, and the value 251 is above the mean. The area under the curve between 41 and 251 is approximately . Similarly, 95.44% of the female students scored between and .