Field Assignment

I’m studying for my Statistics class and don’t understand how to answer this. Can you help me study?

  • An instructor wants to measure the effectiveness of teaching strategies in a class of 30 students. To do so, he selects every third student that arrives in class and providing him or her a questionnaire. Is this an example of random sampling? Explain.
  • The value of the sample mean equals the population mean on average. T/F
  • The value of the sample mean can vary from sample to sample. T/F
  • There is a 0.05 probability of finding a sample mean in a population that is more or less than 2 standard deviations from the population mean. T/F
  • The sampling distribution of sample means is approximately normally distributed. T/F
  • The central limit theorem explains why the mean is always at the center of a distribution. T/F
  • The mean of a sampling distribution is equal to the population mean from which the samples are selected. T/F
  • A college admissions officer indicates that the average GPA of incoming freshmen is normally distributed with a mean of 3.30 and a standard deviation of 0.20. If students with a GPA in the top 10% will be offered a scholarship, what is the minimum GPA required to receive a scholarship? (Hint: determine the z-score for a probability of 0.90, and then rearrange the equation for z-score using that z-score and solving for the value of x.
  • Write the statistical hypotheses for the below after determining if it is one-tailed or two-tailed. A research company concludes that 42% of adults seek advice from a primary care practitioner before seeing a specialist. A researcher wants to test this conclusion.
  • Write the statistical hypotheses for the below after determining if it is one-tailed or two-tailed. A physician makes 5.8 recommendations per day to patients with respect to taking OTC supplements. A researcher believes this is less than the true number of recommendations.
  • Using the z-tables in your text, determine the proportion of the standard normal distribution that lies between each of the following.
    • The mean and z = 1.96
    • The mean and z = 0
    • z = -1.50 and z = 1.50
    • z = -0.30 and z = -0.15
  • State whether the first area below is bigger, the second area is bigger or the two areas are equal on the standard normal distribution.
    • The area to the left of z = 1.00 and the area to the right of z = -1.00.
    • The area to the left of z = 1.00 and the area to the left of z = -1.00.
    • The area between the mean and z = 1.20 and the area to the right of z = 0.80.
    • The area between the mean and z = 1.20 and the area between z = ±1.00.
  • There are many normal distributions.
    • What are the common features of a normal distribution?
    • What are the unique characteristics of the standard normal distribution?
  • A score distribution has a mean of 20 and a standard deviation of 5.
    • Calculate the z-score for a score of 12.5.
    • What proportion of scores are expected to be lower than 12.5 in the population?
    • What percentage of scores will be between 15 and 25?
    • What is the probability of a score greater than 27 being observed?
  • Write the statistical hypotheses for each of the following after determining if they are one-tailed or two-tailed.
    • A research company concludes that 42% of adults seek advice from a primary care practitioner before seeing a specialist. A researcher wants to test this conclusion.
    • A physician makes 5.8 recommendations per day to patients with respect to taking OTC supplements. A researcher believes this is less than the true number of recommendations.
    • The mean age of nurses has been reported to be 46.2 in a recent study. This seems too young, and another researcher wants to test to determine if the average is greater than this.
    • According to the U.S. Department of Labor, in 2010 the average out-of-pocket expense for a family of four on health expenditures is $3,589 annually. An insurance company commissions a study to determine if this number is still the average out-of-pocket expense.

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