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Basic Business Statistics

  1. 8.5 A market researcher selects a simple random sample of n=100 Twitter users from a population of over 100 million Twitter registered users. After analyzing the sample, she states that she has 95% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the meaning of this statement.
  2. 8.6 Suppose that you are going to collect a set of data, either from an entire population or from a random sample taken from that population.
    a. Which statistical measure would you compute first: the mean or the standard deviation? Explain.
    b. What does your answer to (a) tell you about the “practicality” of using the confidence interval estimate formula given in Equation (8.1)?
  3. 8.7 Consider the confidence interval estimate discussed in Problem 8.5. Suppose the population mean time spent on the site is 36 minutes a day. Is the confidence interval estimate stated in Problem 8.5 correct? Explain.
  4. 8.8 You are working as an assistant to the dean of institutional research at your university. The dean wants to survey members of the alumni association who obtained their baccalaureate degrees five years ago to learn what their starting salaries were in their first full-time job after receiving their degrees. A sample of 100 alumni is to be randomly selected from the list of 2,500 graduates in that class. If the dean’s goal is to construct a 95% confidence interval estimate for the population mean starting salary, why is it not possible that you will be able to use Equation (8.1) on page 279 for this purpose? Explain.
  5. 8.9 A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon.
    a. Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle.
    b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company about the amount of water that the bottles contain? Why?
    c. Must you assume that the population amount of water per bottle is normally distributed here? Explain.
    d. Construct a 95% confidence interval estimate. How does this change your answer to (b)?

Sample Solution

g Saudi Arabia. Evidently, oil is one of Venezuela’s most valuable commodities accounting for 95% of Venezuela’s exports and 25% of its gross domestic product (Independent 2018). However, during a period of time in which the global price of oil dropped, foreign demand to buy Venezuelan oil dipped simultaneously. A key factor that lead to Venezuela’s current crisis, is evidently their sole dependence on a single commodity – oil. As University of Florida’s Gamarra explains, this means “you are bound to the ups and downs of the oil price,”. Without a range of high value added assets, an economy lacks diversity and is vulnerable to ‘moments of downturns in your principal commodities (CNBC 2019).’ On an individual basis, hyperinflation renders any savings worthless due to its eroding impact on money. Consequently, people may hoard goods for instance, food due to the soaring prices. Situations such as these may lead to shortages of food supply, contributing to the issue further. The Bolívar (Venuzuelan currency) depreciated in value as the cost of imports increased, leaving the Venezuelan economy to perish. Consequently, Nicolas Maduro – Venezuela’s new president – decided to print money (TheConversation 2019). Although this is an efficient strategy to implement during times of temporary price shock, in the case of Venezuela, the desired results didn’t adhere. Alongside the price of oil continuing to decrease, Venezuela’s oil output also fell resulting in international investors looking elsewhere further decreasing the value of the Bolívar. The government proceeded to print off more money in order to pay their expenses, inevitably resulting in the cycle that lead to hyperinflation (TheConversation 2019). To begin with, whether or not inflation is always deemed to be a challenge or if there are actually any potential benefits surrounding the macroeconomic issue will be discussed. Generally speaking, moderate inflation has some benefits, especially when it’s compared to deflation. For instance, the real value of debt decreases, moderate rates also enable prices of goods to adjust to their real value prices. In some cases, at levels of moderate inflation, companies are able to increase wages whilst the prices of goods increases. However, the average inflation target is usually around 2% which is quite contrasting to that of Venezuela’s. Long term economic growth is thought to be optimised when price stability is maintained, which is done by controlling inflation (Investopedia 2019). At the level of inflation currently being faced by Venezuela, it is more suitable to refer to it as hyperinflation – a more extreme inflation during which price increases are uncontrollable and the value of money erodes to the extent that it is rendered worthless (thebalance 2019). Under these circumstances, few people benefit, however, debt holders and individuals who had taken out loans are amongst those who do, as inflation has the effect of eroding debt. Depending on the spread and severity of the inflation, the increase in prices ma

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