Statistics Normal Distribution Worksheet Paper Homework Help

Question Description

Homework 4

This homework assignment covers material that is discussed in chapters 7 and 8 of the course. Turn in your answers to these questions only!

  1. A normal distribution has a mean of μ = 54 and a standard deviation of σ = 6.
    1. What is the probability of randomly selecting a score less than X = 51?
    2. What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51?
    3. What is the probability of selecting a sample of n =36 scores with a mean less than M = 51?
  • By definition, jumbo shrimp are those that require between 10 and 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages μ = 12.5 with a standard deviation of σ = 1.5, and forms a normal distribution. What is the probability of randomly picking a sample of n =25, 1-pound bags that average more than M = 13 shrimp per bag?
  • A random sample is obtained from a normal population with a mean of μ = 76 and a standard deviation of σ 20. The sample mean is M = 84.
    • Is this a representative sample mean or an extreme value for a sample of   n = 25 scores?
    • Is this a representative sample mean or an extreme value for a sample of   n = 5 scores?
  • Explain the difference between Type I and Type II errors.
  • If the alpha level is changed from α = .05 to α = .01,
    • what happens to the boundaries for the critical region?
    • what happens to the probability of a Type I error?
  • Ackerman and Goldsmith (2011) report that students who study from a screen (phone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from printed pages. To test this finding, a professor identifies a sample of n = 16 students who used the electronic version of the course textbook and determines that this sample had an average score of M = 72.5 on the final exam. During the previous three years, the final exam scores for the general population of students taking the course averaged μ =77 with a standard deviation of σ = 8 and formed a roughly normal distribution. The professor would like to use the sample to determine whether students studying from an electronic screen had exam scores that are significantly different from those for the general population.
  • Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined.
  • Using the standard four-step procedure, conduct a two-tailed hypothesis test with α to evaluate the effect of studying from an electronic screen.
  • Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 15. The sample of group-participation adolescents had an average of M = 53.8.
    • Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with α.
    • Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.
  • A random sample is selected from a normal population with a mean of μ =40 and a standard deviation of σ = 6. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 37.
    • If the sample consists of n = 36 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05
    • If the sample consists of n =9 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.
    • Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.

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