1. Economic periods of prosperity followed by recession are described as: A. Secular trend B. Seasonal variation C. Cyclical variation D. Erratic variation 2. The following linear trend equation was developed for annual sales from 1995 to 2001 with 1995 the base or zero year. = 500 + 60t (in $thousands). What are the estimated sales for 2005 (in $thousands)? A. $500 B. $560 C. $1,040 D. $1,100 3. Which one of the following is not a component of a time series? A. Secular trend B. Moving average C. Seasonal variation D. Irregular variation E. All of the above are components 4. The possible values for the Durbin-Watson statistic are A. any value B. any value greater than zero C. any value from 0 to 4 inclusive D. any value less than zero. 5. A question has these possible choices—excellent, very good, good, fair and unsatisfactory. How many degrees of freedom are there using the goodness-of-fit test to the sample results? A. 0 B. 2 C. 4 D. 5

6. What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories? A. 3.841 B. 5.991 C. 7.815 D. 11.070 7. What is our decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed value is 6.079? A. The difference is probably due to sampling error; do not reject the null hypothesis B. Not due to chance; reject the null hypothesis C. Not due to chance; do not reject the alternate hypothesis D. Too close; reserve judgment 8. The chi-square distribution is A. positively skewed. B. negatively skewed. C. normally distributed. D. negatively or positively skewed. 9. Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution? A. 3 degrees B. 12 degrees C. 15 degrees D. All would 10. If the...

...that we are accepting the alternative hypothesis and this statement works vice versa. In this case that means that the null hypothesis can be rejected or disproving. For the data set that was given the null hypothesis also known as H-nought was µ1=µ2, while the alternative hypothesis is µ1<µ2. Null hypothesis states that the amount of rural nurse homes was equal to the average amount of beds used. Alternative hypothesis states that rural area nursing homes uses fewer amounts of beds. The claim indicated to what kind of test was going to be used and since I claimed that the rural area were going to have a lower average number of beds it states that the shaded area on the critical value test will be less than zero.
Table 1. Descriptive statistics for the given null and alternative hypothesis that includes the sample, mean, median, standard deviation, maximum values, and minimum values.
Sample Size
Mean
Median
Standard Deviation
Maximum Value
Minimum Value
Rural Area
34
0.6538
1.0000
0.4803845
1
0
Bed
4850
93.27
88.00
40.85273
244.00
25.00
Figure 1. This figure illustrates the critical value test for the left-tailed test. The critical value that was needed for the test was -1.692 according to the t-table since our sample size was 34. Used the degree of freedom formula to find the critical value.
Figure 2. This figure reflects to the p-value. When we figured out the p-value we used pt(t,33). Since pt(t,33) equaled 0.0137855 that indicated...

...Charismatic Condition
Mean 4.204081633
Standard Error 0.097501055
Median 4.2
Mode 4.8
Standard Deviation 0.682507382
Sample Variance 0.465816327
Kurtosis 5.335286065
Skewness -1.916441174
Range 3.5
Minimum 1.5
Maximum 5
Sum 206
Count 49
Confidence Level(95.0%) 0.196039006
In both the Charismatic and the punitive condition data sets there were 49 people surveyed. We know this because we were able to use descriptive statistics to show the count and that shows the number of people surveyed. The average or the mean of the charismatic condition is 4.20. The standard error is saying that 0.0975 % is the error that will normally occur if two different people are comparing results. The middle value or the median of the data set is 4.2 and the most frequently occurring value or mode is 4.8. The charismatic condition is skewed to the left because we are getting a negative number for the skewness data. The skewness is at -1.916441174. The difference between the largest and the smallest value which is also called the range is 3.5. The minimum score is 1.5 and the maximum score was a 5 given by the students for the charismatic condition.
The Frequency for the charismatic condition is telling us the summary of the data that is presented is the form of class intervals and frequency. This bar graph will show you the values of the scores starting at 1.5 and going up to 5. The frequency shows us the number of students who picked the...

... |148 |
|Seat belts not worn |283 |330 |
6. Referring to Table 12-1, which test would be used to properly analyze the data in this experiment?
a) test for independence.
b) test for difference between proportions.
c) ANOVA F test for interaction in a 2 x 2 factorial design.
d) test for goodness of fit.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: chi-square test of independence
7. Referring to Table 12-1, the calculated test statistic is
a) -0.9991.
b) -0.1368.
c) 48.1849.
d) 72.8063.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: chi-square test of independence, test statistic
8. Referring to Table 12-1, at 5% level of significance, the critical value of the test statistic is
a) 3.8415.
b) 5.9914.
c) 9.4877.
d) 13.2767.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: chi-square test of independence, critical value
9. Referring to Table 12-1, at 5% level of significance, there is sufficient evidence to conclude that the
a) use of seat belts in motor vehicles is related to ethnic status in San Diego County.
b) use of seat belts in motor vehicles depends on ethnic status in San Diego County.
c) use of seat belts in motor...

...Hypotheses:
H₀: μ=94.4
H₁: μ>94.4
Rejection Region:
Degree of freedom:
d.f=n-1
=49
t> ta,d.f
t>0.05,49
t>1.6766
Test statistics:
t=
From using the Data Analysis Plus in Excel we get:
t-Test: Mean
Cleanser Spending
Mean
102.4000
Standard Deviation
27.5711
Hypothesized Mean
94.4
df
49.0000
t Stat
2.0517
P(T1.6766).
2)
± ta/2,d.f s/
From using the Data Analysis Plus in Excel we get:
t-Estimate:Mean
Cleanser Spending
Mean
102.4000
Standard Deviation
27.5711
LCL
94.5645
UCL
110.2355
We estimate that the mean amount spent over one year lies between $94.56 and $110.26and when we divided by 4 we get the mean amount spent for every 3 month:
We estimate that the mean amount spent for every 3 month lies between $23.64 and $27.56. This estimate is 95% correct of the time
Case 2:
1)
Hypotheses:
H₀: μ=142
H₁: μ≠ 142
Rejection Region:
Degree of freedom:
d.f= n-1
=23
tta/2,d.f
tt0.05,23
t17139
Test statistic:
t=
From using the Data Analysis Plus in Excel we get:
t-Test: Mean
Hot Chocolate
Mean
141.3750
Standard Deviation
1.9959
Hypothesized Mean
142
df
23
t Stat
-1.5341
P(T9
Rejection Region:
Degree of freedom:
d.f= n-1
= 23
χ² > χ²a,d.f
χ² > χ² 0.1, 23
χ² > 32.0069
Test statistic:
χ²=
From using the Data Analysis Plus in Excel we get:
Chi Squared Test:...

...1 Statistics plays a vital role in almost every facet of human life. Describe the functions of Statistics.Explain the applications of statistics.
Meaning of statistics
Functions of statistics
Applications of statistics.
Ans:Statistics plays an important role in almost every facet of human life. In business context, managers are required to justify decisions on the basis of data. They need statistical models to support these decisions. Statistical skills enable managers to collect, analyse and interpret data in order to take suitable decisions.
Defination of statistics. “Statistics is a science which deals with the method of collecting, classifying, presenting, comparing and interpreting the numerical data to throw light on enquiry”. – Seligman
Prof. Boddington, on the other hand, defined Statistics as “The science of estimates and probabilities”2. This definition is not complete.
According to Croxton and Cowden, “Statistics is the science of collection, presentation, analysis and interpretation of numerical data from logical analysis”3.
Function of statistics: Statistics is used for various purposes. It is used to simplify mass data and to make comparisons easierLet us look at each function of Statistics in detail.
1. Statistics simplifies mass data
The use of statistical concepts...

...How many standard deviations is my hypothesis (sample mean) is away from the actual (null hypothesis population mean)
T – statistic
Rejecting the null may be a mistake = p –value
ONE SAMPLE
3 formulas
T.Dist.rt (t, sample size - 1 “df”) -> alternative that mu is bigger than a
1 – T.Dist.rt (t, sample size – 1) -> mu is less than a
T.Dist.2t(t,samplesize - 1) -> not equal to
p < significant level reject the null
NEVER accept null
TWO SAMPLE
directly get the p-value
chance that under the null hypthoesis, you have a difference in the sample mean that is as extreme or more as what you have now. If that probability is small, it is something in the nature not due to chance.
* Paired: T.Test (sample 1, sample 2, # of tails , 1)
* not equal to: number of tails = 2
* greater than or less than: number of tails = 1
* Type 1 = paired data (ex: every UNC mba student’s salary before they entered the program and salaries after graduate )
* salaries have a significant increase after mba?
*
* Independent: T.Test (sample 1, sample 2, # tails, 2)
* Type 2 = independent (ex: UNC mbas vs. DUKE mbas)
*
*
*
* Regression Coefficient:
*
* Null hypothesis: THIS regression coefficient = 0
* alternative hypothesis: THIS particular regression coefficient of interest is not 0
*
* (driver’s p-value and coefficient in ANOVA)
*
* THIS driver’s p-value is less than...

...The T-Test
Page 1 of 4
Home » Analysis » Inferential Statistics »
The T-Test
The t-test assesses whether the means of two groups are statistically different from
each other. This analysis is appropriate whenever you want to compare the means of
two groups, and especially appropriate as the analysis for the posttest-only two-group
randomized experimental design.
Figure 1. Idealized distributions for treated and comparison group posttest values.
Figure 1 shows the distributions for the treated (blue) and control (green) groups in a
study. Actually, the figure shows the idealized distribution -- the actual distribution
would usually be depicted with a histogram or bar graph. The figure indicates where
the control and treatment group means are located. The question the t-test addresses
is whether the means are statistically different.
What does it mean to say that the averages for two groups are statistically different?
Consider the three situations shown in Figure 2. The first thing to notice about the
three situations is that the difference between the means is the same in all three But, you
three.
should also notice that the three situations don't look the same -- they tell very
different stories. The top example shows a case with moderate variability of scores
within each group. The second situation shows the high variability case. the third
shows the case with low variability. Clearly, we would conclude that the two groups...

...sample observations are influenced by some non-random cause.
Hypothesis Tests
Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called hypothesis testing, consists of four steps.
State the hypotheses. This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false.
Formulate an analysis plan. The analysis plan describes how to use sample data to evaluate the null hypothesis. The evaluation often focuses around a single test statistic.
Analyze sample data. Find the value of the test statistic (mean score, proportion, t-score, z-score, etc.) described in the analysis plan.
Interpret results. Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null hypothesis, reject the null hypothesis.
Decision Errors
Two types of errors can result from a hypothesis test.
Type I error. A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level. This probability is also called alpha, and is often denoted by α.
Type II error. A Type II error occurs when the researcher fails to reject a null hypothesis that is false. The probability of committing a Type II error is called Beta, and is often...