[Review Question]: In your own words, explain what the margin error is? How do the confidence level, sample size and population stand deviation (sigma) affect the margin error?

[Review Question]: How to explain the statement “the 95% confidence interval is [1,3]?” Justify each of the following interpretation (why it is right or wrong?)

A) 95% of the values in the population is between 1 and 3.

B) 95% of the values in the sample is between 1 and 3.

C) 95% of sample means in the sampling distribution is between 1 and 3.

D) 95% of population mean is between 1 and 3.

[Review Question]: List conditions (assumptions) for the z-method and t-method, and then point what the major difference between the two.

[Review Question]: What is standard error and what does it measure? Do you want a smaller or bigger standard error in general?

StatsPortal>Statistical videos: StatClips: sampling distributions: overview and motivation part II

[Review Question]: Given and , what is the mean and standard deviation of the sample mean? I.e., and .

[Review Question]: CLT is based on multiple samples, and sampling distribution. But in a real study, we have only data from one sample, how can we use a single sample to estimation the population parameter?

StatsPortal>assignment>Stattutor: margin of error and confidence interval

[Review Question]: A 90% confidence interval for µ is (11.5, 12.3). What is the probability that the value of µ is in this interval?

[Review Question]:The higher the level of confidence you choose, the ____(more/less) ”sure” you can be that mu will be in the confidence interval. The _____(more/less) precise, or _____(wider/narrower) you interval will be.

1. A shipment of 1000 small lab mice arrives at the animal care facility with the weight **following a skewed distribution (****.** A sample of 40 mice is selected and weighed. The sample average weight is 10.2 g, and the sample standard deviation is 2 g.

a. What are the population and sample in this question?

b. Since we know the , we can compute the confidence interval with the Z-method.What is the margin error?

c. Compute and interpret a **90%** confidence interval for the mean weight of all the mice in the shipment.

2. What critical value t* would you use for a confidence interval for the mean of the population in each of the following situations?

a. A 95% confidence interval based on n=10 observations.

b. A 99% confidence interval from an simple random sample of 20 observations.

c. An 80% confidence interval from a sample of size 7

3. A student in wildlife management studied trout habitat in the upper Shavers Fork watershed in West Virginia. The springtime water pH of 29 randomly selected tributary sample sites was found to have the following values:^{6}

a. What is the standard error of the mean.

b. Use a 90% confidence interval to estimate the mean springtime water pH of the tributary water basin around the Shavers Fork watershed

4. A dendritic tree is a branched structure that emanates from the body of a nerve cell. In a study of brain development, researchers examined brain tissue from 36adult guinea pigs. The investigators randomly selected nerve cells from a certain region of the brain and counted the number of dendritic branch segments emanating from each selected cell. A total of 36 cells (1 per pig) was selected, and the resulting counts were as follows:

measurement |
|||

28 |
24 |
38 |
25 |

42 |
26 |
29 |
45 |

25 |
26 |
49 |
28 |

35 |
47 |
26 |
31 |

35 |
28 |
41 |
46 |

33 |
24 |
26 |
32 |

48 |
35 |
35 |
39 |

53 |
38 |
38 |
59 |

17 |
26 |
44 |
53 |

a) Construct a 95% confidence interval for the population mean of dendrite branch segments (The variable can be seen as continuous in this case).

b) Suppose you want to estimate the population mean to be within 2 cells, how many pigs should be examed?

7[OQ] Create a confidence interval problem and specify why you should use the Z-method or T-method. Provide solution to your question and attach your data set.