An economist is interested in studying the monthly incomes of consumers in a particular region. The population standard deviation of monthly income is known to be R1000. A random sample of 55 individuals resulted in an average monthly income of R15000. What is the upper end point in a 99% confidence interval for the average monthly income in this region? Select one: a. R15332 b. R15314 c. R15328 d. none of the above e. R15347
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- A study of 96 bolts of carpet showed that their average length was 77.5 yards. The standard deviation of the population is 1.6 yards. Which of the following is the 90% confidence interval for the mean length per bolt of carpet?A regional airline serving Las Vegas has a base airfare rate of $99. In addition, various fees are charged: for checked baggage, refreshments/drinks in-flight, and for making a reservation on its website. These additional charges average $70 per passenger. Suppose a random sample of 59 passengers is taken to determine the total cost of their flight. The population standard deviation of total flight cost is known to be $40. (a) What is the population mean cost per flight in dollars? $ (b) What is the probability the sample mean will be within $10 of the population mean cost per flight? (Round your answer to four decimal places.) (c) What is the probability the sample mean will be within $5 of the population mean cost per flight? (Round your answer to four decimal places.)In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected from 64 randomly selected customers. The sample mean was calculated as $27.75 with a sample standard deviation of $4. We wish to develop a 91% confidence interval for the mean amount spent per customer for dinner at this restaurant. Assume that the standard deviation of the amounts spent by ALL customers is $4.30. What is the variable of interest? ["", "", ""] And is this variable Quantitative or Qualitative? ["", ""] In other words: what is the one piece of info we care about for each individual in the population? Is it a quantitative measurement? Or do we determine if each individual belongs to a certain category (referred to as success) or not (failure)? If it is a quantitative measurement, then the population is filled with numbers. Otherwise, the population is filled with…
- A researcher is interested in finding a 90% confidence interval for the mean number of times per day that college students text. The study included 97 students who averaged 25.5 texts per day. The standard deviation was 20.5 texts. Round answers to 3 decimal places where possible. b. With 90% confidence the population mean number of texts per day is between ______ and _______ texts. c. If many groups of 97 randomly selected members are studied, then a different confidence interval would be produced from each group. About _______ percent of these confidence intervals will contain the true population number of texts per day and about ___________ percent will not contain the true population mean number of texts per day.Find the 90% confidence interval for the variance and standard deviation of the ages of students at Arcanum high school if a sample of 24 students has a standard deviation of 2.3 years. Assume the variable is normally distributed.The standard deviation, S, for the annual medical cost of 24 households was found to equal $1689 find a 95% confidence interval for the standard deviation of the annual medical cost for all households. Assume medical costs are normally distributed.
- Consider a small scale example, comparing how temperatures have changed in the US from 1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. The locations are the same for both years. The difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.24 degrees with a standard deviation of 4.25 degrees. We are interested in determining whether this provides strong evidence of temperature warming in the continental US. (Does the data provide evidence that the true mean temperature is greater in 2008 than in 1968?) Justify by using a confidence interval or a hypothesis test with α = 0.05. What type of error are you in danger of making?A manufacturer advertises that the average life of batteries produced by his firm is at least 12 months. The consumer board disagrees, and claims that the average life of the batteries is less than 12 months. The consumer board test a random sample of 9 batteries and find that the mean life is 10.6 months with a standard deviation of 2. The consumer board's alternative hypothesis is: A. The average life of the population of batteries is 12 months. B. The average life of the population of batteries is less than 12 months. C. The average life of the population of batteries is more than 12 months. D. The average life of the population of batteries is at least 12 monthsThe manufacturer of 'Road King' tyres claim that their tyres last an average of 70,000km or more. The Consumer Board suspects that this claim may be false (they have received some complaints) and decide to test the manufacturer's claim. The Consumer Board took a sample of size 500 from the population. They ran the…Suppose we wish to calculate a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2. Assume that the amount spent on books by freshmen has a normal distribution with a standard deviation of $30. How many observations are required to achieve this margin of error?
- Twelve samples of coal from a Northern Appalachian source had an average mercury content of 0.253 ppm with a standard deviation of 0.029 ppm. Suppose the density of mercury content of coal from this source is approximately normally distributed. a. Find the LOWER bound of a 95% confidence interval for the mean mercury content of coal from this source. b. Find the UPPER bound of a 95% confidence for the mean mercury content of coal from this source.2. The average gasoline price of one of the major oil companies has been $1.00 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $1.04. Assume that the standard deviation of the population (o) is $0.12. a) State the null and the alternative hypotheses for testing the belief. b) Describe a Type I error and a Type II error for this situation. c) What is the critical value at a = .05? d) what's your What is the t-statistic or z-statistic associated with the above sample results?A study is done to determine if students in the California state university (CSU) system take longer to graduate, on average, than students enrolled in private universities using the significant level of 5%. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years for CSU and 1 year for private universities. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3. What is the decision rule of rejecting the null hypothesis