Please show your solution step by step for each problem to receive partial points for wrong answers. Question 1 (10 points) Briefly and concisely describe in your own words the following: What is the...

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Please show your solution step by step for each problem to receive partial points for wrong answers.



Question 1 (10 points)



Briefly and concisely describe in your own words the following:




  1. What is thez-score and why it is important in inferential statistics. Give at least two reasons. (2 pts)




  2. All the characteristics of the normal distribution curve and how it is used in probability problems. Give at least two uses. (2 pts)




  3. The central limit theorem and the standard error of the mean. (2 pts)




  4. Why there should be both a null hypothesis (Ho) and an alternative hypothesis in research design. Give at least one reason for each (don’t just give the definition of each hypothesis). (2 pts)




  5. What is Type I error and why one commits a Type I error. Give two reasons. (2 pts)





Question 2 (18 points)



The Grade 11 class obtained µ= 80 and σ= 5 in English, and µ= 75 and σ= 5 in History.




  1. Find thez-score of a score (X) that is (a.1) 10 points above and another that is (a.2) 8 points below the English µ; (a.3) 7 points above and (a.4) 8 points below the History µ. (4 pts)




  2. Determine the raw scores corresponding to the followingz-scores in History: (b.1) z = -1.65, and (b.2) z = 1.96. (4 pts)




  3. You obtained a raw score of 95 in English and 90 in History. Compared to the entire class, in which course did you do better? Briefly explain your answer. (5 pts)




  4. 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 85 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. (5 pts)





Question 3 (12 points)



A researcher is randomly selecting a sample for his experiment from a group of 40 high school students, 40 college students, and 10 graduate students. Each group is equally divided between males and females. State probabilities in %.




  1. What is the probability of selecting a college student? (2 pts)




  2. What is the probability of selecting a graduate student? (2 pts)




  3. What is the probability of selecting a male high school student? (2 pts)




  4. If the researcher selects a stratified random sample of n = 20, how many will be high school students in this sample? (3 pts)




  5. What is the probability of selecting a female college student to be part of the small random sample of 20? (3 pts)





Question 4 (20 points)



Assume that the distribution of scores in a Statistics test is normal, with µ = 100 and σ = 15.




  1. What is the probability that a score is 120? (Hint:Find thez-scores of the real limits and the difference between the probabilities.) (4 pts)




  2. What is the probability that a score is below 90? (4 pts)




  3. What is the probability that a score is between 130 and 85? (Hint:Find the z-score of each, then combine the probabilities.) (4 pts)




  4. What is the percentile rank of X = 105? (Hint:The answer is based on thez-score of X = 105.) (4 pts)




  5. What proportion of the scores is above the 80th percentile? (Hint: This is a conceptual question to determine your understanding of percentile; no solutions required.) (4 pts)





Question 5 (20 points)



The average number of products that the assembly line workers at Style-X Company assemble per day is µ = 40 with a standard deviation of σ = 15. Assume that the distribution of units assembled is normal. If a sample n = 25 were drawn from all of the workers:




  1. What range of units manufactured by this sample would contain the sample mean 90% of the time? (Hint:First find the middle 90% of the distribution of sample means.) (5 pts)




  2. What is the probability that the sample mean will be between 35 and 49 units? (5 pts)




  3. Is it reasonable for this sample to produce an average of 44 products per day, or is this mean very different from what would be normally expected? (5 pts)




  4. How likely is it that this sample will produce more than an average of 55 products per day? (5pts)





Question 6 (20 points)



A researcher would like to test the effectiveness of using imagery to improve the memory of a sample of n = 49 Grade 7 students. Assume that the mean score on a standardized memory test of all the Grade 7 students in Maple Elementary School last year is µ = 75% with σ = 10. The sample, after learning how to use imagery for 10 weeks obtained a mean of M = 80%. Conduct a hypothesis test, by calculating thez-score, at α = .05, for a two-tailed test. Show all the five steps.


Answered 1 days AfterOct 15, 2021

Answer To: Please show your solution step by step for each problem to receive partial points for wrong answers....

Pooja answered on Oct 16 2021
119 Votes
Please show your solution step by step for each problem to receive partial points for wrong answers.
Question 1 (10 points)
Briefly and concisely describe in your own words the following:
A. What is thez-score and why it is important in inferential statistics. Give at least two reasons. (2 pts)
B. All the characteristics of the normal distribution curve and how it is used in probability problems. Give at least two uses. (2 pts)
C. The central limit theorem and the standard error of the mean. (2 pts)
D. Why there should be both a null hypothesis (Ho) and an alternative hypothesis in research design. Give at least one reason for each (don’t just give the definition of each hypothesis). (2 pts)
E. What is Type I error and why one commits a Type I error. Give two reasons. (2 pts)
a)
z score is a measure of position that indicates the measure of standard deviation a data value lies from the mean. If z-score is positive, raw score lies above mean. If z-score is negative, the raw score lies below the mean.
Uses of z score are:
1. To calculate probability of score occurring within normal distribution
2. Enables to compare two score that are from different scales
b)
characteristics
1. Curve is symmetrical and asymptote
2. Mean = median = mode
3. Total Area under the normal curve is 1.
c)
Central limit theorem states that when sample size is large (n>30), sampling distribution of sample mean is normal.
Mathematically, if X follows normal with (mu, sd)
Then, Xbar follows Normal (mu, sd/sqrt(n))
Here, the standard error of the mean is defined by sd/sqrt(n)
d)
Null hypothesis is neutral statement about population parameter. The alternative hypothesis is the claim of the researcher.
Consider a scenario to test if weight decreases after treatment.
Here, null hypothesis, Ho: there is no significant difference in the mean weight between before and after treatment. (mu1=mu2)
This is tested against alternative hypothesis, h1: the mean weight before treatment is higher than after treatment. (mu1>mu2)
e)
Type I error = P(reject Ho | Ho is true)
It is also known as level of significance. It is defined as probability of rejecting the null hypothesis when it is true.
· We want to control the type I error and hence set it at a predefined level of significance. generally alpha is set as 5%
· Since type I error is more danger than type II error, it is controlled by defining at a predefined level of significance.
Question 2 (18 points)
The Grade 11 class obtained µ= 80 and σ= 5 in English, and µ= 75 and σ= 5 in History.
A. Find thez-score of a score (X) that is (a.1) 10 points above and another that is (a.2) 8 points below the English µ; (a.3) 7 points above and (a.4) 8 points below the History µ. (4 pts)
B. Determine the raw scores corresponding to the followingz-scores in History: (b.1) z = -1.65, and (b.2) z = XXXXXXXXXXpts)
C. You...
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