Question

Assignment 1 Part A - Confidence Intervals and Hypothesis Testing
(One Population)
1. The shoulder height for a random sample of six (6) fawns (deer less than 5 months old) in a national park was , ? = 79.25 cm with population standard deviation ?= 5.33 cm. Compute an 80% confidence interval for the mean shoulder height of the population of all fawns (deer less than 5 months old) in this national park. Analyze the result to interpret its meaning. (10 points)

2. A random sample of 732 judges found that 405 were introverts. Construct a 95% confidence interval for the proportion. Interpret the meaning of the confidence interval. Justify your use of a confidence interval based on a normal distribution for data regarding proportions that are normally following a binomial distribution. (10 points)

3. It has been determined that 37 out of 100 adult Americans that did not attend college believe in extra-terrestrials. However, from a random sample of 100 adult Americans that did not attend college 43 claim that they believe in extra-terrestrials. Does this indicate that the proportion of people who did not attend college and who believe in extra-terrestrials has changed? Conduct a hypothesis test with a = 0.01 and interpret the results. (10 points)

Assignment 1 Part B – Inference (Two Populations), Chi-Squared Tests
1. In a study of brain waves during sleep, a sample of 29 college students were randomly separated into two groups. The first group had 15 people and each was given ½ liter of red wine before sleeping. The second group had 14 people and were given no alcohol before sleeping. All participants when to sleep at 11 PM and their brainwave activity was measured from 4-6 AM. The group drinking alcohol had a mean brainwave activity of 19.65 hertz and a standard deviation of 1.86 hertz. The group not drinking alcohol had a mean of 6.59 hertz and standard deviation of 1.91 hertz. Compute a 90% confidence interval for the difference in population means of groups drinking alcohol before sleeping and those not drinking alcohol before sleeping. Explain the meaning of the confidence interval. (10 points)
2. Discuss the following: (10 points)
 What type of data can be examined using the Chi-Squared Test?
 What is the only constraint in using Chi-Squared Tests?
 What problems can be caused by the way the data have been grouped?

Answer 1

1. The shoulder height for a random sample of six (6) fawns (deer less than 5 months old) in a national park was , ? = 79.25 cm with population standard deviation ?= 5.33 cm. Compute an 80% confidence interval for the mean shoulder height of the population of all fawns (deer less than 5 months old) in this national park. Analyze the result to interpret its meaning.

Sample size = n = 6

Sample mean = = 79.25

Population standard deviation = = 5.33

We have to construct 80% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.28    ( Using z table)

So confidence interval is ( 79.25 - 2.7852 , 79.25 + 2.7852) = > ( 76.4648 , 82.0352)

Interpretation:

We are 80% confidence that the population mean shoulder height of the population of all fawns (deer less than 5 months old) in this national park lies in  ( 76.4648 , 82.0352).