# STATS 230 QUIZ 3

- How do we calculate the standard error of the mean?

- Sample standard deviation divided by square root of sample size
- Square root of sample variance
- Square root of population variance
- Sample standard deviation divided by sample size

- Which of the following description of the standard error of the mean is correct?

- The standard error of the mean is the standard deviation of the sampling distribution of the mean
- The standard error of the mean is the squared variance of the sampling distribution of the mean
- Standard error is the sample standard deviation
- Standard error is the same with population standard deviation

- The sample standard deviation is 50, and the sample size is 400. What’s the standard error of the mean?
**(Show work)**

- Which of the following is correct according to the Central limit theorem?

- As the sample size increases, the sample distribution of the mean is closer to the population distribution
- As the sample size increases, the sample distribution of the mean is closer to the normal distribution regardless of whether or not the distribution of the population is normal
- As the sample size increases, the sample distribution of the mean is closer to the normal distribution but only when the distribution of the population is normal
- As the sample size increases, the sample distribution of the mean is closer to the population distribution regardless of whether or not the population distribution is normal

- Imagine a high school of 1,000 students. The school administrator wants to know the average height of students in that school. However, he does not know if it makes a difference if he samples more students or less. Thus, your suggestion for him is:

- As you measure more students, the standard error will be smaller
- As you measure more students, the average height will be smaller
- As you measure more students, the variance of sample distribution will be bigger
- As you measure more students, the standard deviation of the sample distribution will be bigger.

- The mean of the sampling distribution of the means is___ the mean of the population from which the values were sampled.

- Equal to
- Smaller than
- Bigger than
- Equal to or smaller than

- Imagine that in California, the average weight of boys in 7th grade is 100 lbs and the standard deviation of the mean is 4. A researcher selected several different samples from this population. What would the standard deviation of the sampling distribution of the mean be for N=100?
**(Show work)**

- Imagine that a total of 100 students took a Statistics quiz. If we randomly selected 25 students, their average grade was 80 and variance of the sampling distribution of the mean was 5. What will be the variance of the sample distribution of the mean if we randomly select 50 students:
**(Show work)**

- Imagine for the national college admission test, women had a mean score of 70 and a variance of 16; men had a mean score of 69 and a variance of 25. If we sample 50 scores from women and 50 scores from men, what’s the standard error of sample distribution of the difference between means?
**(Show work)**

- Imagine that the correlation between years of education and income in a population was 0.55. Imagine we sampled 19 people and obtained a correlation coefficient of 0.45. What’s the standard error of Z’ for N=19?
**(Show work)**

- Imagine you have a population of 100,000 cases. For which of the following degrees of freedom, can you generate the most accurate estimation of the population parameter?

- 10
- 20
- 50
- 2000

- Two hundred students took a standard chemistry test. You sampled 20 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the standard deviation?

- 21
- 20
- 19
- 40

- Which of the following descriptions of “bias” is correct?
**(Select all that apply)**

- A sampling method is biased if each element does not have an equal chance of being selected.
- A sampling method is biased if every element is selected
- An estimator is biased if it systematically overestimates or underestimates the parameter it is estimating
- An estimator is biased if it overestimates but does not underestimates the parameter

- _____ is the statistic that refers to how much the estimate varies from sample to sample.

- Sample variance
- Mean
- Median
- Standard error

- A company just purchased 1,000 flat screen TVs. From the product label, the weight of one TV should be 15.4 pound. The manager of the company randomly selected 20 TVs and measured their weights. Then, he repeated this procedure again three times. The means and standard errors are listed as follows. Which sample estimate shows
**the least****sample variability**?

- Sample one: mean=16.0, SE=1.0
- Sample two: mean=15.0, SE=0.6
- Sample three: mean=16.5, SE=1.5
- Sample four: mean=17.0, SE=2.0

- A company just purchased 1,000 flat screen TVs. From the product label, the weight of one TV should be 15.4 pound. The manager of the company randomly selected 20 TVs and measured their weight. Then, he repeated this procedure again three times. The means and standard errors are listed as follows. Which sample estimate shows
**the least bias**?

- Sample one: mean=16.0, SE=1.0
- Sample two: mean=15.0, SE=0.6
- Sample three: mean=16.5, SE=1.5
- Sample four: mean=17.0, SE=2.0

- A teacher wanted to know the average weight of students in her class. She randomly sampled four students and obtained their weights. They were 120 lbs., 100 lbs., 90 lbs, and 130 lbs. What’s the standard error of the mean from our sample estimate?
**(Show work)**

- Imagine a researcher wanted to know the average years of education of the adult population in a certain community. He randomly sampled nine adults and obtained the mean years of education was 7 and the
**standard error**of the mean was 3. What’s the lower limit for the 95% of the confidence interval of the mean?**(Show work)**

- The t distribution becomes closer to a normal distribution when the degrees of freedom___.

- Increase
- Decrease
- First Increase and then decrease
- First decrease and then increase

- Which of the following choices are the possible confidence intervals on the population values of a Pearson’s correlation r?
**(Select all that apply)**

- (0.92, 0.99)
- (-0.87, 0.9)
- (-1.4, 0.3)
- (0.89, 1.23)