1. (12 points) In this recession, yours truly would like to make extra money to support his frequent filet-mignon-et-double-lobster-tail dinner habit. A promising enterprise is to mass-produce garnet wedding rings for brides. Based on my diligent research, I have found out that women's ring size normally distributed with a mean of 6.0, and a standard deviation of 1.0. I am going to order 5000 garnet wedding rings from my reliable Siberian source. They will manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5. How many wedding rings should I order for each of the ring size if I order 5000 rings altogether? (Note: It is natural to assume that if your ring size falls between two of the above standard manufacturing size, you will take the bigger of the two.)

2. (8 points) According to a study by my PseudoScientific Consulting, the time interval between Atlantic hurricane of category 4 has a mean of 456 days and a standard deviation of 123 days. Suppose that you observe a sample of five (5) time intervals between successive category 4 hurricanes. a. On average, what would you expect to be the mean of the five (5) time intervals? b. How much variation would you expect from your answer in part (a)? (Hint: Think along the line of the Empirical 68-95-99.7 Rule.)

The following information is for Questions 3 through 8.
The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is 2.4 µg (micrograms). My brother takes it upon himself to make sure that everyone gets the recommended daily allowance. It is generally believed that growing teens are getting less than the RDA of 2.4 µg of cobalamine daily. It is an open secret that my brother's Au & Associates FauxPharmaceutical (AFP) peddles dietary supplements around the globe. It is claimed by representatives of AFP that by taking their vitamin supplement extracted from Atlantic scrod, brand-named as...

...CHAPTER 4 – THE BASIS OF STATISTICALTESTING
* samples and populations
* population – everyone in a specified target group rather than a specific region
* sample – a selection of individuals from the population
* sampling
* simple random sampling – identify all the people in the target population and then randomly select the number that you need for your research
* extremely difficult, time-consuming, expensive
* cluster sampling – identify clustering units in the population
* opportunity sampling – selecting participants who just happen to be available at the time and the place that you are conducting your research
* snowball sampling – referrals from participants
* volunteer sampling – where you might advertise your study and wait for people who have read your ad to come forward to take part
* how generalizable are data?
* Q: are the means for our sample approximately equal to the mean from the population?
* randomly selected sample because of this random factor, sample may not be exactly representative
* sampling error
* the difference between the sample mean and the population mean
* ensure that you have enough participants so that you get an accurate reflection of the population that you are interested in
* population mean (parameter), sample mean (statistic)
* the larger the...

...click “OK”. (See the 3 figures, below.)
6.
Your output should look like this.
7.
You should use the output information in the following manner to answer the question.
Step 0 : Check Assumptions The samples were taken randomly and independently of each other. The populations have approximately the same shapes (according to the boxplots). All sample sizes are at least 6 if k = 3 (smallest is 6). Hypotheses
Step 1 :
H0 : M1 = M2 = M3 (The median test scores are equal.) Ha : Not all of the medians are equal.
Step 2 : Step 3 : Step 4 :
Significance Level Rejection Region Reject the null hypothesis if p-value ≤ 0.05. Test Statistic
α = 0.05
Note that the test statistic (KW = Chi-Square = 7.5023) is corrected for the existence of ties in the ranks of the data.
Step 5 : Step 6 :
Decision Since p-value = 0.0235 ≤ 0.05 = α, we reject the null hypothesis. State conclusion in words At the α = 0.05 level of significance, there exists enough evidence to conclude that there is a difference among the three teaching methods based on the test scores.
...

...report aims to analyse and interpret the data set of 200 records regarding the CCResort. The given information includes booking identification number, income, number of people per booking, length of stay, age and overall expenditure.
From the booking ID it can be assumed that the selection of data is random, however as it is only partial information and not the population, the period of time in which the data is selected from would affect the end results of analysis.
The report is divided into two sections outlining the statistical analysis of data and hypothesistesting to observe if CCResort have met their 2 major key performance indicators (KPIs)
1 More than 40% of their customers stay for a full week (i.e. seven nights);
2 The average customer spends more than $255 per day in excess of accommodation costs.
Figures at a glance
This section of the report aims to give users a better understanding of the data through statistical data analysis of investigation categories including family income, expenditure habits, age distribution, the number of people per booking and their length of stay. These analysis are meaningful in giving users a better understanding of the customer base in relation to the key performance indicators.
1. Family income distribution
From the data collected, 62 families (31% of the sample) earn an income of more than $100,000 while 69% of the sample (138...

...Why We Don’t “Accept” the Null Hypothesis
by Keith M. Bower, M.S. and James A. Colton, M.S.
Reprinted with permission from the American Society for Quality
When performing statisticalhypothesis tests such as a one-sample t-test or the AndersonDarling test for normality, an investigator will either reject or fail to reject the null
hypothesis, based upon sampled data. Frequently, results in Six Sigma projects contain
the verbiage “accept the null hypothesis,” which implies that the null hypothesis has been
proven true. This article discusses why such a practice is incorrect, and why this issue is
more than a matter of semantics.
Overview of HypothesisTesting
In a statisticalhypothesis test, two hypotheses are evaluated: the null (H0) and the
alternative (H1). The null hypothesis is assumed true until proven otherwise. If the
weight of evidence leads us to believe that the null hypothesis is highly unlikely (based
upon probability theory), then we have a statistical basis upon which we may reject the
null hypothesis.
A common misconception is that statisticalhypothesis tests are designed to select the
more likely of two hypotheses. Rather, a test will stay with the null hypothesis until
enough evidence (data) appears to...

...Running head: MULTIPLE SAMPLE HYPOTHESISTESTING
Multiple Sample HypothesisTesting
RES342: Research 11
June 14, 2010
Multiple Sample HypothesisTesting
The purpose of this paper is to create a hypothesis based on two-sample tests. Two-sample tests compare two sample estimates with each other, whereas one-sample tests compare a sample estimate with a non-sample benchmark (Doane & Seward, 2007). The learning team has chosen to create a hypothesistesting using the wages and wage earners data set. The learning team has developed one business research question from which the team will formulate a research hypothesis. The business research question and testing simply involves creating two separate groups of the data set, and testing whether a difference in the mean of the earnings in both the older group, ages 42-64 and the younger group, ages 18-41 exists. To create a solid testinghypothesis, the team has formulated both a numerical and verbal hypothesis statement, conducted the five-step hypothesis test on the data, and presented a description of the test results by explaining how the discoveries from the hypothesistesting can be used to answer the research question.
Learning Team A believes that there are...

...Question 4
Hypothesis Tests of a Single Population
1. Explain carefully the distribution between each of the following pairs of terms:
a) Null and alternative hypotheses
b) Simple and composite hypotheses
c) One-sided and two-sided alternatives
d) Type I and Type II errors
e) Significance level and power
2. During 2000 and 2001 many people in Europe objected to purchasing genetically modified food that was produced by farmers in the United States. The U.S. farmers argued that there was no scientific evidence to conclude that these products were not healthy. The Europeans argued that there still might be a problem with food.
a) State the null and alternative hypotheses from the perspective of the Europeans.
b) State the null and alternative hypotheses from the perspective of the U.S. farmers.
3. Bank cash machine need to be stocked with enough cash to meet demand over an entire weekend. However, the bank will lose out on interest payments on any excess cash stocked into the cash machines. A particular bank believes that the mean withdrawal rate per transaction is normally distributed with a mean of $150 and a standard deviation of $50. Is there any evidence that the bank has got its calculations wrong, if a random sample of 36 customer transactions gives a mean sample of $160? State your null and alternative hypotheses.
4. A random sample is obtained from a population with varianceσ2=625, and the sample mean is...

...27 April 2014
Submission date: 9 May 2014
TUTORIAL ON HYPOTHESISTESTING (1)
Basic Concept
1. State the null and alternative hypothesis for each conjecture :
a. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 3.0kg.
b. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 8.
c. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean score was 73.
d. The average time to read a certain passage is 15 minutes. An educator claimed that a course in speed reading will shorten the reading time.
e. A chemist said that he invested an additive which can increase the life of batter. The mean lifetime is 24 months.
f. The mean waiting bus for buses in Klang Valley is 8 minutes. Some roads are restricted to buses only during office hours. A test is performed to see how this has affected the mean waiting time.
2. Determine whether the one-tailed test or two-tailed test is appropriate for the situation given below:
a. Testing whether the newly-purposed highway speed limit increases the number of accidents.
b....

...Business Statistics, 9e (Groebner/Shannon/Fry)
Chapter 10 Estimation and HypothesisTesting for Two Population Parameters
1) The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. If the sample size is n = 10 from each population, the samples are independent, and sample standard deviations are used, and the variances are assumed equal, then the critical value will be t = 2.1009.
Answer: TRUE
Diff: 2
Keywords: confidence interval, mean difference, independent, sample
Section: 10-1 Estimation for Two Population Means Using Independent Samples
Outcome: 1
2) To find a confidence interval for the difference between the means of independent samples, when the variances are unknown but assumed equal, the sample sizes of the two groups must be the same.
Answer: FALSE
Diff: 2
Keywords: confidence interval, mean difference, independent
Section: 10-1 Estimation for Two Population Means Using Independent Samples
Outcome: 1
3) The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. Assume that the variances are equal and the populations normally distributed. The following data represent independent samples from each...