Inferential Statistics - Normal Distribution Curve - Statistics Assignment Help

Assignment Task :

Question 1

Briefly and concisely describe in your own words the following: 

a. The z-score and why it is important in inferential statistics. Give at least 2 reasons.

b. Characteristics of the normal distribution curve and how it is used in probability problems. Give at least 2 uses. 

c. The central limit theorem and the standard error of the mean. 

d. Why there should be a Null hypothesis (Ho) in research design. Give at least 1 reason. 

e. Why one commits a Type I error. Give at least 1 reason.

Question 2 

History.

a. Find the z-score of a score (X) that is (a.1) 5 points above and another that is (a.2) 6 points below the English µ; (a.3) 7 points above and (a.4) 8 points below the History µ. 

b. Determine the raw scores corresponding to the following z-scores in History: (b.1) z = -1.65 (b.2) z = 1.96. 

c. You obtained a raw score of 90 in both English and History. Compared to the entire class, in which course did you do better? Briefly explain your answer. 

d. Assume that both the English and the History tests were transformed into a standardized distribution with µ= 100 and σ= 15. If Paul’s raw score of 80 in both original tests are standardized, in which course did he do better? Show his new scores after being transformed into the standardized distribution. Briefly explain your answer. 

Question 3 

A researcher is randomly selecting a sample for his experiment from a group of 30 high school students, 20 college students, and 10 graduate students. Sixty percent of each group are females and forty percent are males.

a. What is the probability of selecting a college student? 

b. What is the probability of selecting a graduate student? 

c. What is the probability of selecting a male high school student?

d. If the researcher selects a stratified random sample of n = 10, how many will be high school students?

e. Among the high school students selected in this random sample of 10, what is the probability of selecting a female? 

Question 4 

Assume that the distribution of scores in a Math test is normal, with µ = 100 and σ = 10. What is the probability that:

a. A score is 125? (Hint: find the z-scores of the real limits and the difference between their probabilities.)

b. A score is below 80?

c. A score is between 125 and 80? 

e. Above the 75th percentile? 

Question 5 

The average number of units that the factory workers at Shilo Company assemble per week is µ = 45 with a standard deviation of σ =12. Assume that the distribution of units assembled is normal. If a sample n = 25 were drawn from all of the workers:

a. What range of units manufactured by this sample would contain the sample mean 90% of the time? (Hint: find the middle 90% of the distribution of sample means.) 

b. What is the probability that the sample mean will be between 40 and 50 units?

c. Is it reasonable for this sample to produce an average of 48 units per week, or is this mean very different from what would be normally expected? 

d. How likely is it that this sample will produce more than an average of 55 units? 

Question 6 

A researcher would like to test the effectiveness of using mnemonics to improve the memory of a sample of n = 36 Grade 9 students. Assume that the mean score on a 

standardized memory test of all the Grade 9 students in Jersey Secondary School last year is µ = 78% with σ = 10. The sample, after learning how to use the mnemonic for 10 weeks obtained a mean of M = 84%. Conduct a hypothesis test, by calculating the z-score, at α = .05, for a two-tailed test. Show all the five steps.

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