General Motors is conducting a market analysis to determine whether they are paying their employees the market rate. In particular, they would like to construct a 90% confidence interval of the average executive salary, +/-$1,000. They know from a nationwide study that the standard deviation of salaries is $15,500. What is the minimum sample size necessary to obtain this estimate?

On the PSAT test taken by about 1.5 million high school juniors each year, the mean score on the reading portion of the test was 46.9, with a standard deviation of 10.9. The scores are normally distributed. If a student needed a score on this portion of the test that put them in the top 5% of scores nationally to qualify for a particular scholarship, what is the minimum score they must achieve?

Nutrition Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 56 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.40 mg with standard deviation 4.71 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.41 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. You can use the Inferential Statistics page and the Distribution Calculators page in SALT to answer parts of this question. (a) State the hypotheses (in mg) that we can use to consider this question. (Enter != for as needed.) Ho: H₁: (b) Carry out the hypothesis test in part (a) using the critical-value method with an a level of 0.05, and summarize your findings. Find the test statistic. (Round your answer to two decimal places.) Find the…

The president of an all-female school wants to know if the students at her school studied more or less, on average, than the students at a neighboring all-male school. To find out, she conducted a study. Accordingly, samples were taken at each school with the following results: All female: sample size = 43, mean study time ( hours) = 18.56, standard deviation (hours) = 4.35 All male: sample size = 38, mean study time (hours) =17.95, standard deviation (hours) = 4.87 Calculate the 95% confidence interval for the differences between population means. Use brackets write the final answer [x.xx, x.xx]

Fuel efficiency of Prius:  Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the standard deviation is 5.2 MPG. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed. (a) The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? The test statistic is: __________________(please round to two decimal places)The p-value:___________________________ for this hypothesis test is:  (please round to four decimal places)(c) Please comment on the primary thing that is wrong about the following statement: There is sufficient evidence…

Exercise 3. A personal manager has found that historically the scores on aptitude tests given to applicants for entry-level positions follow a normal distribution with a standard deviation of 32.4 points. A random sample of nine test scores from the current group of applicants had a mean score of 187.9 points. a. Find an 80% confidence interval for the population mean score of the current group of applicants. b. Based on these sample results a statistician found for the population mean a confidence interval extending from 165.8 to 210.0 points. Find the confidence level of this interval.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. The survey yields several scores, one of which measures student attitudes toward studying. The mean student attitude score for college students is about 30, and standard deviation is about 12. A researcher in the Philippines is concerned about the declining performance of college graduates on professional licensure and board exams. She suspects that poor attitudes of students are partly responsible for the decline and that the mean for college seniors who plan to take professional licensure or board exams is less than 30. She gives the SSHA to an SRS of 144 college seniors in the Philippines who plan to take professional licensure or board exams. Suppose we know that the student attitude scores in the population of such students are Normally distributed with standard deviation σ = 12. (a) We seek evidence against the claim that μ = 30. What is the…

Beer Drinking. The mean annual consumption of beer per person in the US is 22.0 gallons . A random sample of 300 Washington D.C. residents yielded a mean annual beer consumption of 27.8 gallons. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean annual consumption of beer per person for the nation’s capital differs from the national mean? Assume that the standard deviation of annual beer consumption for Washington D.C. residents is 55 gallons.