Investment Returns:These data are the annual returns on shareholders’ funds of 97 of Australian’s top 100 companies for the years 1990 and 1998.

(i)Produce a histogram of the 1990 returns.

(ii)Produce a histogram of the 1998 returns.

(iii)Find the mean, median, range and standard deviation for the 1990 returns. Annual Returns % (1990)
Mean12.91865979
Median11.38
Standard Deviation9.297513067
Range75.01

(iv)Repeat part (iii) for the 1998 returns.
Annual Returns % (1998)
Mean6.355463918
Median5.4
Standard Deviation5.170830853
Range42.76

(v)Which was the better year for investors?
•1990 was the better year for investors in regards to annual returns being consistent with the mean of 12.9% compare to 6.4% for 1998. •The measure of variability was high in 1990 with the range of 75.01 compare to 42.76 for 1998. Another high variability for 1990 was the standard deviation of 9.30 compare to 5.17 for 1998.

(For Excel instructions see pages 28 and 61 of the textbook.)

Question 2.(Statistical Inferences: Single Population)

Feasibility Study: Companies that sell groceries over the Internet are called e-grocers. Customers enter their orders, pay by credit card and receive delivery by truck. To determine whether an e-grocery would be profitable in one large city, a potential e-grocer offered the service and recorded the size of the order for a random sample of customers. The data are stored in the data file.

(i)Estimate with 95% confidence the average order in the city. Orders ($)
Mean89.16511905
Confidence Level (95.0%)3.770623926

(ii)Financial analysis indicates that to be profitable the average order would have to exceed $85. Can we infer from the data that an e-grocery will be profitable in the city? Test using = 0.01.

Step 1: Hypothesis is that to be profitable the average order has to exceed $85. Since it’s unproven, it is the alternative hypothesis. The null...

...Inferences for One Population StandardDeviation
The Standarddeviation is a measure of the variation (or spread) of a data set. For a variable x, the standarddeviation of all possible observations for the entire population is called the population standarddeviation or standarddeviation of the variable x. It is denoted σx or, when no confusion will arise, simply σ. Suppose that we want to obtain information about a population standarddeviation. If the population is small, we can often determine σ exactly by first taking a census and then computing σ from the population data. However, if the population is large, which is usually the case, a census is generally not feasible, and we must use inferential methods to obtain the required information about σ.
In this section, we describe how to perform hypothesis tests and construct confidence intervals for the standarddeviation of a normally distributed variable. Such inferences are based on a distribution called the chi-square distribution. Chi is a Greek letter whose lowercase form is χ. A variable has a chi-square distribution if its distribution has the shape of a special type of right-skewed curve, called a chi-square (χ2) curve. Actually, there are infinitely many chi-square distributions,...

...potentially skew the results in that maybe those that didn’t answer were employed and busy at work giving the unemployed more chances of answering their calls.
6. Write the null and alternative hypothesis corresponding to the given claim. Identify the test as left-tailed, right-tailed, or two-tailed.
a) A battery maker claims their top selling battery will last, on average, at least 50 hours.
Ho: μ ≥ 50hrs (claim)
Ha: μ < 50hrs It is left tailed.
b) The mean body temperature of baboons = 98.6°.
Ho: μ = 98.6° It is a two-tailed test.
Ha: μ ≠98.6°
c) The majority of the American adults support Healthcare reform.
Ho: p ≤ 50% It is right tailed
Ha: μ > 50%
d) The standarddeviation for human body temperatures is less than 0.02°
Ho: σ ≥ 0.02° It is left tailed
Ha: σ < 0.02°
7. Claim: The mean test score on a given test is greater than 165 points.
Sample statistics: n=85, 172, and s=35
a) Identify the null and alternative hypothesis for the given claim
Ho: p≤ 165 points
Ha:p > 165 Points
b) Identify the critical value(s) and the rejection region(s) for =0.05
Zo =1.645 and the rejection region is the area right of Zo (that is if you are facing the graph)
c) Determine the value of the test statistic and the outcome of the test for the given statistics.
Ans: Z = 1.84
d) Interpret the outcome of the test in the context of the...

...Chapter 10
StatisticalInferences Based on Two Samples
True/False
1. An independent sample experiment is an experiment in which there is no relationship between the measurements in the different samples.
Answer: True Difficulty: Medium
2. When testing the difference between two proportions selected from populations with large independent samples, the Z test statistic is used.
Answer: True Difficulty: Medium
3. In forming a large sample confidence interval for [pic], two assumptions are required: independent samples and sample sizes of at least 30.
Answer: True Difficulty: Medium
4. In testing the equality of population variances, two assumptions are required: independent samples and normally distributed populations.
Answer: True Difficulty: Medium
5. In an experiment involving matched pairs, a sample of 12 pairs of observations is collected. The degree of freedom for the t statistic is 10.
Answer: False Difficulty: Medium
6. When comparing two independent population means, if n1 = 13 and n2 = 10, degrees of freedom for the t statistic is 22.
Answer: False Difficulty: Easy
7. When comparing the variances of two normally distributed populations using independent random samples, if [pic], the calculated value of F will always be equal to one.
Answer: True Difficulty: Easy
8. In testing the difference between two population variances, it is a common practice to compute the F statistic so that...

...rejected? a=7.7
97, 101, 99, 99, 100, 94, 87, 99, 108, 93, 96, 88, 98, 97,88, 105, 97, 96, 98, 102, 99, 94, 96, 114, 99, 96, 98, 97, 91, 98, 80, 95, 98, 96, 80, 95, 88, 99, 102, 95, 101, 94, 92, 99, 101, 97, 94, 97, 102, 61.
The claim can be rejected; correct answer may be either above 98 or below it.
2. Salaries for Actuaries nationwide graduates entering the actuarial field earn $40,000. A college placement officer feels that this number is too low. She surveys 36 graduates entering the actuarial field and finds the average salary to be $41,000. The population standarddeviation is $3000. Can her claim be supported at 0.05?
x¯=14.7, μx¯=13.77, ox¯=5.34, n=29, α=.01
3. Monthly Home Rent. The average monthly rent for a one bedroom in San Francisco is $ 1229. A random sample of 15 one bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population standarddeviation is $250. At a=0.05 can we conclude that the monthly rent outside San Francisco differs from that in the city?
4.
5. Federal Prison Populations nationally 60.2% of federal prisons are severing time for drug offenses. A warden feels that in his prisons the percentage is even higher. He surveys 400 inmates records and finds that 260 of the inmates are drug offenders at a=0.05 is this correct?
CHAPTER 9
1.
Driving for pleasure - two groups of drivers is surveyed to see how many miles per week...

...Standarddeviation can be difficult to interpret as a single number on its own. Basically, a small standarddeviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standarddeviation means that the values in the data set are farther away from the mean, on average.
The standarddeviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standarddeviation.
A small standarddeviation can be a goal in certain situations where the results are restricted, for example, in product manufacturing and quality control. A particular type of car part that has to be 2 centimeters in diameter to fit properly had better not have a very big standarddeviation during the manufacturing process. A big standarddeviation in this case would mean that lots of parts end up in the trash because they don’t fit right; either that or the cars will have problems down the road.
But in situations where you just observe and record data, a large standarddeviation isn’t necessarily a bad thing; it just reflects a large amount of variation in the group that is being studied. For example, if you look at salaries for everyone in a...

...Deviation
Definition:
Behavior commonly seen in children that is the result of some obstacle to normal development such behavior may be commonly understand as negative (a timid child, a destructive child) or positive (a quite child), both positive and negative deviation will disappear once the child begins to concentrate on a piece of work freely chosen by him.
The physical deforms are easier to identify. This can be by birth due to an accident etc… and most such physical deforms can be either cured. However, deforms that take place in development of psychological aspects of a child are not only threat to building the character and the personality of the child also you find certain physical deforms in curable in medicine.
Dr. Montessori, according to her she fugues deviated children are.
The naughty children act and react very strong as a result of severe treatment they have received. So their behavior is cruel from others.
The weak children are always mistaken for good children and parent are happy because of their timidly and but they are lazy and afraid of everything.
The bright children are very imaginative and live in their own fantasy world.
Deviations shown by the strong and weak children are:
In the absorbent mind Montessori discussed deviation shown by the strong, meaning those who resist and overcome the obstacles they meet and deviation...

...I'll be honest. Standarddeviation is a more difficult concept than the others we've covered. And unless you are writing for a specialized, professional audience, you'll probably never use the words "standarddeviation" in a story. But that doesn't mean you should ignore this concept.
The standarddeviation is kind of the "mean of the mean," and often can help you find the story behind the data. To understand this concept, it can help to learn about what statisticians call normal distribution of data.
A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other.
Let's say you are writing a story about nutrition. You need to look at people's typical daily calorie consumption. Like most data, the numbers for people's typical consumption probably will turn out to be normally distributed. That is, for most people, their consumption will be close to the mean, while fewer people eat a lot more or a lot less than the mean.
When you think about it, that's just common sense. Not that many people are getting by on a single serving of kelp and rice. Or on eight meals of steak and milkshakes. Most people lie somewhere in between.
If you looked at normally distributed data on a graph, it would look something like this:
The x-axis (the horizontal one) is the value in question......

...StandardDeviation (continued)
L.O.: To find the mean and standarddeviation from a frequency table.
The formula for the standarddeviation of a set of data is [pic]
Recap question
A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box):
[pic].
Calculate the mean and standarddeviation for x.
Introductory example for finding the mean and standarddeviation for a table:
The table shows the number of children living in a sample of households:
|Number of children, x |Frequency, f |xf |x2f |
|0 |14 |0 × 14 = 0 |02 × 14 = 0 |
|1 |12 |1 × 12 = 12 | |
|2 |8 | | |
|3 |6 | |32 × 6 = 54 |
|TOTAL |[pic]...

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