# Various statistical questions

The following questions relate to learning objectives found mostly in week 1. When determining the 95% confidence interval for a population mean with known sigma the value of the critical value of z is equal to
A. 1. 645
B. 1. 96
C. 2. 58
D. it depends on the degrees of freedom
2. The confidence interval for the population mean is ________________?
A. a range of values which probably contains the population mean
B. a range of values which contains the population mean
C. the same from sample-to-sample
D. both a and c
3. How can you tell if a hypothesis is a 1 or a 2 tail test?

We can tell if a hypothesis is a 1 or a 2 tail test by looking Alternate hypothesis. If Alternate hypothesis involves symbol ‘’ (greater than) than the hypothesis is 1 tail test. If it involves symbol ‘≠’ (not equal to) than the hypothesis is 2 tail test.
4. Correctly state the Null and Alternative hypotheses for the following: “ The owner of Books R Us wants to see if the mean of a recent sample of sales data for the first and second quarters is greater than the average sales data benchmark he’s been using.”
The Null hypothesis is that the mean of a recent sample of sales data for the first and second quarters is NOT greater than the average sales data benchmark used (μ0). In symbols:
H0: μ ≤ μ0
The Alternate hypothesis is that the mean of a recent sample of sales data for the first and second quarters is greater than the average sales data benchmark used (μ0). In symbols:
H1: μ > μ0
_
5. In the equation X –  = and “ X –  =”, what is the difference in what we are measuring?
The equation is measuring the difference between sample mean and population mean. Whereas, the equation is measuring the difference between an individual value in the sample and population mean.
6. True/False: Ho:  = 0; H1:  not = 0 would call for a two-tail test. True
7. With which test statistic do we need to worry about degrees of freedom: The Z or the T statistic?
With T statistic, we need to worry about degrees of freedom.
8. A problem statement is a question about the possible relationship between the __Independent__ and ___Dependent___ variables in a situation where we believe a relationship exists between the variables.
9. True/False – The P-Value is the probability of observing a sample value as extreme, or more extreme than, the value observed given that we accept that the Null Hypothesis is true. True
10. If our null hypothesis is Ho: u1 = u2, this is a problem where we wish to use a two-sample test of means. Which of the following is NOT TRUE :
A. We assume the samples are independent
B. We assume that n is greater than or equal to 30
C. We want to see if the difference between the two sample means is not equal to 0
D. We would use a Chi Square distribution with n-k degrees of freedom
11. True/False – When we have a two-tail Z test at the 95% confidence level, we want to divide the α by 2 to determine the critical value. True
12. In the formula,
Define:
a. S2Sample variance
b. X1 First sample mean
c. X2 Second sample mean
d. n1 First sample size
e. n2 Second sample size
13. True/False – A paired sample population test is used for the independent samples. False
A paired sample population test is used for the dependent samples.
14. There are two types of dependent samples: Those that measure something before and after an “ event” and those that matching two samples of the same phenomena being observed. Which of the following is NOT true about such a test:
a. We calculate the mean of the differences between the paired observations
b. We must calculate the standard deviation of their paired observation differences.
c. The variation of the differences of the paired samples is greater than when the two samples are considered to be independent of each other. This will result in a smaller likelihood of rejecting the null hypothesis.
d. The standard error of the paired, dependent statistic will result in a higher likelihood of rejecting the null hypothesis.
15. The basic strategy of ANOVA is to:
a. Estimate the variation 2 ways and find their ratios. If the ratio = 1. 0, then the variations are different and we reject the Null Hypothesis.
b. Estimate the variation 2 ways and find their ratios. If the ratio = 1. 0, then the variations are the same and we fail to reject the Null Hypothesis.
c. Calculate their variations and divide by n-2. If the quotient is > 1. 0, then the variations are different and we reject the Null Hypothesis.
d. Calculate their variations and divide by n-2. If the quotient is less than or = 1. 0, then the variations are the same and we fail to reject the Null Hypothesis.
16. True/False – The F distribution is used to test whether two or more samples are from populations having equal variances. False
17. True/False – To figure out the degrees of freedom in an ANOVA table, we take n-k degrees of freedom in the numerator, and k-1 degrees of freedom in the denominator. False
18. Which of the following assumptions are required for ANOVA?
a. Each population is normally distributed
b. The populations have equal variances
c. The errors are both random and independent
d. All of the above.
19. True/False – A theory is a statement about a population parameter developed for testing. True
20. True/False – When plotting a trend equation, the dependent variable is plotted along the horizontal axis. False
21. True/False – Correlation analysis is the study of the relationship between variables. True
22. True/False – A correlation of -. 25 is weaker than a correlation of +. 15. False
23. If the coefficient of determination is 0. 87, what percentage of the variation of the model is not explained?
a. 10%
b. 13%
c. 87%
d. 90%
24. If the slope of a line is 2. 2 and the y intercept is 37, what is the equation that describes the line?
a. y = 37x
b. y = 37x + 2. 2
c. y = 2. 2x + 37
d. x = 2. 2 + 37y
25. If the points in scatter diagram generally tended from upper left to lower right, you would conclude that the correlation was probably
a. positive
b. negative
c. zero or close to zero
d. the answer can’t be determined from the information available
26. If there are four independent variables in a multiple regression equation, there are also four:
a. Y-intercepts
b. Regression coefficients
c. F-values
d. Coefficients of determination
e. All of the above.