REVIEW EXERCISES
CHAPTER 8 AND 9
PROFESSOR JONAS
WIURES
BY DEBRA JAMES
CHAPTER 8
1. High temperature in the United States a meteorologist claims that the average of the highest temperatures in the united states in 98. A random sample of 50 cities is selected, and the highest temperatures are recorded. The data are shown. At a=0.05 can the claim be 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 standard deviation 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 standard deviation 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 they drive for pleasure trips. The data are shown at a=0.01 can it be conducted that single drivers do more driving for pleasure trips on average than married drivers? Assume =16.7 and =16.1 Level...
...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) Onesided and twosided 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 standarddeviation 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...
...Question 1. (Descriptive Statistics)
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 standarddeviation for the 1990 returns.
Annual Returns % (1990)
Mean 12.91865979
Median 11.38
StandardDeviation 9.297513067
Range 75.01
(iv) Repeat part (iii) for the 1998 returns.
Annual Returns % (1998)
Mean 6.355463918
Median 5.4
StandardDeviation 5.170830853
Range 42.76
(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 standarddeviation 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 egrocers. Customers enter their orders, pay by credit card and receive delivery by truck. To determine whether an egrocery would be profitable in one large city, a...
...Case 2: Gulf Real Estate Properties. Please provide a Managerial Report that includes: 1. Appropriate descriptive statistics to summarize each of the three variables for the forty Gulf View condominiums 2. Appropriate descriptive statistics to summarize each of the three variables for the eighteen NoGulf View condominiums 3. Comparison of your summary results from #1 & #2. Discuss any specific statistical results that would help a real estate agent understand the condominium market. 4. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. 5. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. Also, consider the following scenario and include your responses in your Report: 6. Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of NoGulf View condominiums with a margin of effort of $15,000. Using 95% confidence, how large should the sample sizes be?
GULF VIEW CONDOMINIUMS
List Price Sales Price Days to Sell
495000 475000 130
379000 350000 71
529000 519000 85
552500 534500 95
334900 334900 119
550000 505000 92
169900 165000 197
210000 210000...
...serving to be 78 with a sample standarddeviation of 7.
State the null and alternative hypotheses. 

 A. H0: = 75, H1: ≠ 75  

 B. H0: 75, H1: > 75  

 C. H0: 75, H1: < 75  

 D. H0: = 75, H1: > 75  
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Question 6 of 10  1.0 Points 
Consider the following scenario in answering questions 5 through 7. In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standarddeviation of 7.
Compute the z or t value of the sample test statistic. 

 A. z = 1.916  

 B. t = 1.916  

 C. t = 1.916  

 D. z = 1.645  
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Question 7 of 10  1.0 Points 
Consider the following scenario in answering questions 5 through 7. In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with...
...Practical 16: estimating Population Size Using Mark and Recapture Method
Raw and Processed Data
Table 1: Uncertainties of apparatus used in the experiment.
Apparatus  Uncertainties 
Stopwatch  ±0.01s 
Table 2: Formulae and sample calculations involved in processing data in the experiment.
Calculations  Formula  Sample Calculation 
Mean
( x )  x = 1n i=1naiWhere, 1. n refers to the total number of values. 2. ∑ refers to the addition of all values starting with the first value, denoted by i = 1, and ending off with the last value, denoted by n. 3. ai refers to the values in sequence from i = 1 to the nth term or last term.  Mean Lincoln Index: x= 15114+127+194+163+172≈154 
StandardDeviation ( σ )  σ=1ni=1nfi(xix)2Where, 1. n refers to the total number of values. 2. ∑ refers to the addition of all values starting with the first value, denoted by i = 1, and ending off with the last value –denoted by n. 3. fi refers to the frequency of that exact term being calculated. 4. (xix)2 refers to the square of the term, denoted by xi, subtracted by the mean value of the terms, denoted by x.  StandardDeviation for Lincoln Index: σ= 15(1141542+1271542+1941542+1631542+(172154)2)≈33.0 
Lincoln Index (Total Population)  Total Population =x1x2x3 Where, 1. x1 refers to the number Of white beads in the first capture. 2. x2 refers to...
...Inferences for One PopulationStandardDeviation
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 populationstandarddeviation 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 populationstandarddeviation. 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 chisquare distribution. Chi is a Greek letter whose lowercase form is χ. A variable has a chisquare distribution if its distribution has the shape of a special type of rightskewed curve, called a chisquare (χ2)...
...Mean and StandardDeviation
The mean, indicated by μ (a lower case Greek mu), is the statistician's jargon for the average value of a signal. It is found just as you would expect: add all of the samples together, and divide by N. It looks like this in mathematical form:
In words, sum the values in the signal, xi, by letting the index, i, run from 0 to N1. Then finish the calculation by dividing the sum by N. This is identical to the equation: μ =(x0 + x1 + x2 + ... + xN1)/N. If you are not already familiar with Σ (upper case Greek sigma) being used to indicate summation, study these equations carefully, and compare them with the computer program in Table 21. Summations of this type are abundant in DSP, and you need to understand this notation fully. In electronics, the mean is commonly called the DC (direct current) value. Likewise, AC (alternating current) refers to how the signal fluctuates around the mean value. If the signal is a simple repetitive waveform, such as a sine or square wave, its excursions can be described by its peaktopeak amplitude. Unfortunately, most acquired signals do not show a well defined peaktopeak value, but have a random nature, such as the signals in Fig. 21. A more generalized method must be used in these cases, called the standarddeviation, denoted by σ (a lower case Greek sigma).
As a starting point, the expression,xiμ, describes how far the ith sample deviates...
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