1) Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market if the new trash bag's mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.9 is x=50.575. If we let u denote the mean of the breaking strengths of all trash bags of the new type and assume that o equals 1.65:

a. Calculate 95 percent and 99 percent confidence intervals for u. b. Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 50 pounds? Explain c. Using the 99% confidence interval, can we be 99% confident that u is at least 50 pounds? explain d. Based on your answers to parts b and c, how convinced are you that the new 30-gallon trash bag is the strongest such bag on the market?

(a) (i) 95% confidence interval for μ:n = 40x-bar = 50.575s = 1.65% = 95Standard Error, SE = σ/Ön = 0.2609z- score = 1.9600Width of the confidence interval = z * SE = 0.5113Lower Limit of the confidence interval = x-bar - width = 50.0637Upper Limit of the confidence interval = x-bar + width = 51.0863The confidence interval is [50.0637 pounds, 51.0863 pounds](ii) 99% confidence interval for μ:n = 40x-bar = 50.575s = 1.65% = 99Standard Error, SE = σ/Ön = 0.2609z- score = 2.5758Width of the confidence interval = z * SE = 0.6720Lower Limit of the confidence interval = x-bar - width = 49.9030Upper Limit of the confidence interval = x-bar + width = 51.2470The confidence interval is [49.9030 pounds, 51.2470 pounds](b) Yes, we can be 95% confident that μ is at least 50 pounds, since the entire 95% confidence interval lies above 50 pounds (c) No, we can’t be 99% confident that μ is at least 50...

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BUS 308 STATISTICS FOR AMANAGERS
BUS 308 Week 1 DQ 1 Language
Numbers and measurements are the language of business.. Organizations look at results, expenses, quality levels, efficiencies, time, costs, etc. What measures does your department keep track of ? How are the measures collected, and how are they summarized/described? How are they used in making decisions? (Note: If you do not have a job where measures are available to you, ask someone you know for some examples or conduct outside research on an interest of yours.)
BUS 308 Week 1 DQ 2 Levels
Managers and professionals often pay more attention to the levels of their measures (means, sums, etc.) than to the variation in the data (the dispersion or the probability patterns/distributions that describe the data). For the measures you identified in Discussion 1, why must dispersion be considered to truly understand what the data is telling us about what we measure/track? How can we make decisions about outcomes and results if we do not understand the consistency (variation) of the data? Does looking at the variation in the data give us a different understanding of results?
BUS 308 Week 1 Problem Set Week One
Problem Set Week One. All statistical calculations will use the Employee Salary Data set (in Appendix section).
Using the Excel Analysis ToolPak function Descriptive Statistics, generate descriptive statistics for the salary data. Which variables...

...Statistics Cheat Sheet
Proportion = Frequency x 100 = Percentage Total No | Z score (standardised value)-how many sds from the mean the value liesZ score = data value – mean Standard deviation | Metric Data = ExploreCategory = Frequencies |
Bigger sample size will give a narrower confidence interval range (more specific) outliers affect the mean but not the median – this is why the median is preferred here.mean | | Reports -Only give confidence interval if significant-All values to 2 dec pts except the p-value Experimental = IV is manipulated to see the effect on the DV
Observational = Information just observed & recorded |
P-Value Significant Figurep-value < 0.05 = Significantp-value < 0.05 = Not SignificantReport p value 0.000 as <0.001
The probability that our test statistic takes the observed value Always leave at 3 decimal places | Levene’s Test-Used to test if equal variancesIf significant (<0.05)– use equal variances not assumed rowIf not significant (>0.05)– use equal variances assumed rowReport confidence interval as the 95% confidence interval indicates... | Dependent Variable = the variable in which we expect to see a changeIndependent Variable = The variable which we expect to have an effect on the dependent variable Example: There will be a statistically significant difference in graduation rates of at-risk high-school seniors who participate in an...

...Key Synthesis/Potential Test Questions (PTQs)
• What is statistics? Making an inference about a population from a
sample.
• What is the logic that allows you to be 95% confident that the confidence interval contains the population parameter?
We know from the CLT that sample means are normally distributed around the real population mean (). Any time you have a sample mean within E (margin of error) of then the confidence interval will contain . Since 95% of the sample means are within E of then 95% of the confidence interval constructed in this way will contain.
• Why do we use confidence intervals verses point estimates? The sample mean is a point estimate (single number estimate) of the population mean – Due to sampling error, we know this is off. Instead, we construct an interval estimate, which takes into account the standard deviation, and sample size.
– Usually stated as (point estimate) ± (margin of error)
• What is meant by a 95% confidence interval? That we are 95% confident that our calculated confidence interval actually contains the true mean.
• What is the logic of a hypothesis test?
“If our sample result is very unlikely under the assumption of the null hypothesis, then the null hypothesis assumption is probably false. Thus, we reject the null hypothesis and infer the alternative hypothesis.”
• What is the logic of using a CI to do a HT?
We are 95% confident the proportion is in this interval… if the sample mean or...

...G036
* Yes because the p-value is less than 0.05 or No, because the p-value is greater than 0.05
* The coefficient of variation is the standard deviation of a data set, divided by the mean of the same data set.
* Z score = x -ms
* The Independent part is what you, the experimenter, changes or enacts in order to do your experiment. The dependent variable is what changes when the independent variable changes - the dependent variable depends on the outcome of the independent variable.
* P=000=P<0.001
* Repeated measure = A repeated measures design is a longitudinal study, usually a controlled experiment but sometimes an observational study
* We can be 95% confident that on average shoppers at CyberChic are between 3.37 years younger than customers at Modern Miss and 0.75 years older.
* Value of r Strength of relationship -1.0 to –0.5 or 1.0 to 0.5 Strong -0.5 to –0.3 or 0.3 to 0.5 Moderate -0.3 to –0.1 or 0.1 to 0.3 Weak –0.1 to 0.1 None or very weak
One sample t-test
A study was conducted to investigate whether the hours of work has changed for Australian men since 2001.
In a sample of 116 Australian male adults, on average the men worked 39.6 hours per week (s = 4.5). This is higher than the mean of 38.6 hours per week recorded for Australian men in 2001 and a t-test shows that the difference is significant, t (115) = 2.45, p = 0.016. The 95% confidence interval indicates that since 2001 the average hours of work has increased...

...Curve
The Bell Shaped Curve
Mean=Median=Mode
Symmetrical
Asymmetric Curve
Statistical Inference
The Central Limits Theorem: When samples are large (above 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population
Ultimate Goal
Accepting or Rejecting the NULL hypothesis
Accept or Reject?
We accept a null hypothesis when the significance level greater than .05
Reject when less than .05
Confidence Intervals
First you have to know three things:
Statistical inference: the process of using sample statistics to estimate population parameters.
Confidence level: the probability that a population parameter lies within a given confidence interval
Confidence interval: the range of values in which the population parameter is estimated to fall.
A statistic is an estimate of a parameter
But the statistic will rarely equal the parameter exactly.
Because of sample error
If our mean is 64, with a SD of 5, and we want to calculate the 95% confidence interval…
64+(1.96)(5)=73.8
64-(1.96)(5)=54.2
Mean – Z Score – Standard Deviation – 1.96 for 95%
Correlations
Positive or Direct Correlation – change in same direction
Negative or Indirect Correlation – change in opposite direction
Correlations range from -1 to +1
The Absolute value of the correlation represents the strength of the correlation
Strong Correlation =...

...Statistics 1
Business Statistics
LaSaundra H. – Lancaster
BUS 308 Statistics for Managers
Instructor Nicole Rodieck
3/2/2014
Statistics 2
When we hear about business statistics, when think about the decisions that a manager makes to help make his/her business successful. But do we really know what it takes to run a business on a statistical level? While some may think that businessstatistics is too much work because it entails a detailed decision making process that includes calculations, I feel that without educating yourself on the processes first you wouldn’t know how to imply statistics. This is a tool managers will need in order to run a successful business. In this paper I will review types of statistical elements like: Descriptive, Inferential, hypothesis development and testing and the evaluation of the results. Also I will discuss what I have learned from business statistics.
My description of Descriptive statistics is that they are the numerical elements that make up a data that can refer to an amount of a categorized description of an item such as the percentage that asks the question, “How many or how much does it take to “ and the outcome numerical amount. According to “Dr. Ashram’s Statistics site” “The quantities most commonly used to measure the dispersion of the values about...

...
MBA 501A – [STATISTICS]
ASSIGNMENT 4
INSTRUCTIONS: You are to work independently on this assignment. The total number of points possible is 50. Please note that point allocation varies per question. Use the Help feature in MINITAB 16 to read descriptions for the data sets so that you can make meaningful comments.
[10 pts] 1. Use the data set OPENHOUSE.MTW in the Student14 folder. Perform the Chi
Square test for independence to determine whether style of home and location are are related. Use α = 0.05. Explain your results.
Pearson Chi-Square = 37.159, DF = 3, P-Value = 0.000
Likelihood Ratio Chi-Square = 40.039, DF = 3, P-Value = 0.000
The P value associated with out chi square is 0.00 and the Alpha level is 0.05 so we reject the null hypothesis. The P- value is less than the alpha level. So, we conclude that style of homes and locations are not related.
[10 pts] 2. Use the data set TEMCO.MTW in the Student14 folder. Perform the Chi
Square test for independence to determine whether department and gender are related. Use α = 0.05. Explain your results.
Pearson Chi-Square = 1.005, DF = 3, P-Value = 0.800
Likelihood Ratio Chi-Square = 1.012, DF = 3, P-Value = 0.798
The P-value associated with out chi square is 0.800 and the Alpha level is 0.05 we can see that we are unable to reject the null hypothesis. The P- value is greater than the alpha level. So, we conclude that departments and gender are related..
[30 pts] 3. Use the data set...

...Oct. 10, 2012
1. Multiple and True/False Questions (10 points) Please circle the right answer for the questions below. Each question is assigned 2.5 points.
1. The sample mean of population 1 is smaller than that of population 2. If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the a. null hypothesis should state µ1 − µ2 < 0 b. null hypothesis should state µ1 − µ2 ≤ 0 c. alternative hypothesis should state µ1 − µ2 < 0 d. alternative hypothesis should state µ1 − µ2 > 0 ANSWER: c
2.
A Type I error is committed when a. a true alternative hypothesis is not accepted b. a true null hypothesis is rejected c. the critical value is greater than the value of the test statistic d. sample data contradict the null hypothesis ANSWER: b In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with a. n − 1 degrees of freedom
3.
b. c. d. ANSWER: 4.
n degrees of freedom
n − 1 degrees of freedom n degrees of freedom c
The purpose of statistical inference is to provide information about the a. sample based upon information contained in the population b. population based upon information contained in the sample c. population based upon information contained in the population d. mean of the sample based upon the mean of the population ANSWER: b
FMBA SQA Final Exam
Prof. Kihoon Kim Oct. 10, 2012
2. (10 points) A researcher is...