Mathematical Statistics with Applications 7th Edition solutions

Mathematical Statistics with Applications 7
For each of the following situations, identify the population of interest, the inferential objective, and how you might go about collecting a sample. a The National Highway Safety Council wants to estimate the proportion of automobile tires with unsafe tread among all tires manufactured by a specific

Mathematical Statistics with Applications 7
Are some cities more windy than others? Does Chicago deserve to be nicknamed The Windy City? Given below are the average wind speeds (in miles per hour) for 45 selected U.S. cities: 8.9 12.4 8.6 11.3 9.2 8.8 35.1 6.2 7.0 7.1 11.8 10.7 7.6 9.1 9.2 8.2 9.0 8.7 9.1 10.9 10.3 9.6 7.8 11.5 9.3 7.9 8.8 8.8

Mathematical Statistics with Applications 7
Of great importance to residents of central Florida is the amount of radioactive material present in the soil of reclaimed phosphate mining areas. Measurements of the amount of 238U in 25 soil samples were as follows (measurements in picocuries per gram): .74 6.47 1.90 2.69 .75 .32 9.99 1.77 2.41 1.9

Mathematical Statistics with Applications 7
The top 40 stocks on the over-the-counter (OTC) market, ranked by percentage of outstanding shares traded on one day last year are as follows: 11.88 6.27 5.49 4.81 4.40 3.78 3.44 3.11 2.88 2.68 7.99 6.07 5.26 4.79 4.05 3.69 3.36 3.03 2.74 2.63 7.15 5.98 5.07 4.55 3.94 3.62 3.26 2.99 2.74 2.62 7.13 5.

Mathematical Statistics with Applications 7
Given here is the relative frequency histogram associated with grade point averages (GPAs) of a sample of 30 students: 1.85 2.05 2.25 2.45 2.65 2.85 3.05 3.25 3.45 3/30 6/30 0 Relative Frequency Grade Point Average a Which of the GPA categories identified on the horizontal axis are associated with th

Mathematical Statistics with Applications 7
The relative frequency histogram given next was constructed from data obtained from a random sample of 25 families. Each was asked the number of quarts of milk that had been purchased the previous week. 0 .1 .2 .3 .4 0 Relative Frequency 1 2 3 4 5 Quarts a Use this relative frequency histogram to det

Mathematical Statistics with Applications 7
The self-reported heights of 105 students in a biostatistics class were used to construct the histogram given below. 66 69 Heights 60 63 0 5/105 Relative frequency 10/105 72 75 a Describe the shape of the histogram. b Does this histogram have an unusual feature? c Can you think of an explanation for

Mathematical Statistics with Applications 7
An article in Archaeometry presented an analysis of 26 samples of RomanoBritish pottery, found at four different kiln sites in the United Kingdom. The percentage of aluminum oxide in each of the 26 samples is given below: Llanederyn Caldicot Island Thorns Ashley Rails 14.4 11.6 11.8 18.3 17.7 13.8 11

Mathematical Statistics with Applications 7
Resting breathing rates for college-age students are approximately normally distributed with mean 12 and standard deviation 2.3 breaths per minute. What fraction of all college-age students have breathing rates in the following intervals? a 9.7 to 14.3 breaths per minute b 7.4 to 16.6 breaths per min

Mathematical Statistics with Applications 7
Resting breathing rates for college-age students are approximately normally distributed with mean 12 and standard deviation 2.3 breaths per minute. What fraction of all college-age students have breathing rates in the following intervals? a 9.7 to 14.3 breaths per minute b 7.4 to 16.6 breaths per min

Mathematical Statistics with Applications 7
The following results on summations will help us in calculating the sample variance s2. For any constant c, a n i=1 c = nc. b n i=1 cyi = c n i=1 yi . c n i=1 (xi + yi) = n i=1 xi +n i=1 yi . Use (a), (b), and (c) to show that s2 = 1 n 1 n i=1 (yi y) 2 = 1 n 1 n i=1 y2 i 1 n n i=1 yi 

Mathematical Statistics with Applications 7
Use the result of Exercise 1.11 to calculate s for the n = 6 sample measurements 1, 4, 2, 1, 3, and 3.

Mathematical Statistics with Applications 7
Refer to Exercise 1.2. a Calculate y and s for the data given. b Calculate the interval y ks for k = 1, 2, and 3. Count the number of measurements that fall within each interval and compare this result with the number that you would expect according to the empirical rule.

Mathematical Statistics with Applications 7
Refer to Exercise 1.3 and repeat parts (a) and (b) of Exercise 1.13.

Mathematical Statistics with Applications 7
Refer to Exercise 1.4 and repeat parts (a) and (b) of Exercise 1.13.

Mathematical Statistics with Applications 7
In Exercise 1.4, there is one extremely large value (11.88). Eliminate this value and calculate y and s for the remaining 39 observations. Also, calculate the intervals y ks for k = 1, 2, and 3; count the number of measurements in each; then compare these results with those predicted by the empirica

Mathematical Statistics with Applications 7
The range of a set of measurements is the difference between the largest and the smallest values. The empirical rule suggests that the standard deviation of a set of measurements may be roughly approximated by one-fourth of the range (that is, range/4). Calculate this approximation to s for the data

Mathematical Statistics with Applications 7
The College Boards verbal and mathematics Scholastic Aptitude Tests are scored on a scale of 200 to 800. It seems reasonable to assume that the distribution of test scores are approximately normally distributed for both tests. Use the result from Exercise 1.17 to approximate the standard deviation fo

Mathematical Statistics with Applications 7
According to the Environmental Protection Agency, chloroform, which in its gaseous form is suspected to be a cancer-causing agent, is present in small quantities in all the countrys 240,000 public water sources. If the mean and standard deviation of the amounts of chloroform present in water sources

Mathematical Statistics with Applications 7
Weekly maintenance costs for a factory, recorded over a long period of time and adjusted for inflation, tend to have an approximately normal distribution with an average of $420 and a standard deviation of $30. If $450 is budgeted for next week, what is an approximate probability that this budgeted f

Mathematical Statistics with Applications 7
The manufacturer of a new food additive for beef cattle claims that 80% of the animals fed a diet including this additive should have monthly weight gains in excess of 20 pounds. A large sample of measurements on weight gains for cattle fed this diet exhibits an approximately normal distribution with

Mathematical Statistics with Applications 7
Prove that the sum of the deviations of a set of measurements about their mean is equal to zero; that is, n i=1 (yi y) = 0.

Mathematical Statistics with Applications 7
The mean duration of television commercials is 75 seconds with standard deviation 20 seconds. Assume that the durations are approximately normally distributed to answer the following. a What percentage of commercials last longer than 95 seconds? b What percentage of the commercials last between 35 an

Mathematical Statistics with Applications 7
Aqua running has been suggested as a method of cardiovascular conditioning for injured athletes and others who desire a low-impact aerobics program. In a study to investigate the relationship between exercise cadence and heart rate,1 the heart rates of 20 healthy volunteers were measured at a cadence

Mathematical Statistics with Applications 7
The following data give the lengths of time to failure for n = 88 radio transmitter-receivers: 16 224 16 80 96 536 400 80 392 576 128 56 656 224 40 32 358 384 256 246 328 464 448 716 304 16 72 8 80 72 56 608 108 194 136 224 80 16 424 264 156 216 168 184 552 72 184 240 438 120 308 32 272 152 328 480 6

Mathematical Statistics with Applications 7
Compare the ratio of the range to s for the three sample sizes (n = 6, 20, and 88) for Exercises 1.12, 1.24, and 1.25. Note that the ratio tends to increase as the amount of data increases. The greater the amount of data, the greater will be their tendency to contain a few extreme values that will in

Mathematical Statistics with Applications 7
A set of 340 examination scores exhibiting a bell-shaped relative frequency distribution has a mean of y = 72 and a standard deviation of s = 8. Approximately how many of the scores would you expect to fall in the interval from 64 to 80? The interval from 56 to 88?

Mathematical Statistics with Applications 7
The discharge of suspended solids from a phosphate mine is normally distributed with mean daily discharge 27 milligrams per liter (mg/L) and standard deviation 14 mg/L. In what proportion of the days will the daily discharge be less than 13 mg/L?

Mathematical Statistics with Applications 7
A machine produces bearings with mean diameter 3.00 inches and standard deviation 0.01 inch. Bearings with diameters in excess of 3.02 inches or less than 2.98 inches will fail to meet quality specifications. a Approximately what fraction of this machines production will fail to meet specifications?

Mathematical Statistics with Applications 7
Compared to their stay-at-home peers, women employed outside the home have higher levels of high-density lipoproteins (HDL), the good cholesterol associated with lower risk for heart attacks. A study of cholesterol levels in 2000 women, aged 2564, living in Augsburg, Germany, was conducted by Ursula

Mathematical Statistics with Applications 7
Over the past year, a fertilizer production process has shown an average daily yield of 60 tons with a variance in daily yields of 100. If the yield should fall to less than 40 tons tomorrow, should this result cause you to suspect an abnormality in the process? (Calculate the probability of obtainin

Mathematical Statistics with Applications 7
Let k 1. Show that, for any set of n measurements, the fraction included in the interval y ks to y + ks is at least (1 1/k2). [Hint: s2 = 1 n 1  n i=1 (yi y) 2  . In this expression, replace all deviations for which |yi y| ks with ks. Simplify.] This result is known as Tchebysheffs theorem.3

Mathematical Statistics with Applications 7
A personnel manager for a certain industry has records of the number of employees absent per day. The average number absent is 5.5, and the standard deviation is 2.5. Because there are many days with zero, one, or two absent and only a few with more than ten absent, the frequency distribution is high

Mathematical Statistics with Applications 7
For the data discussed in Exercise 1.33, give an upper bound to the fraction of days when there are more than 13 absentees.

Mathematical Statistics with Applications 7
A pharmaceutical company wants to know whether an experimental drug has an effect on systolic blood pressure. Fifteen randomly selected subjects were given the drug and, after sufficient time for the drug to have an impact, their systolic blood pressures were recorded. The data appear below: 172 140

Mathematical Statistics with Applications 7
A random sample of 100 foxes was examined by a team of veterinarians to determine the prevalence of a specific parasite. Counting the number of parasites of this specific type, the veterinarians found that 69 foxes had no parasites of the type of interest, 17 had one parasite of the type under study,

Mathematical Statistics with Applications 7
Studies indicate that drinking water supplied by some old lead-lined city piping systems may contain harmful levels of lead. Based on data presented by Karalekas and colleagues,4 it appears that the distribution of lead content readings for individual water specimens has mean .033 mg/L and standard d

Mathematical Statistics with Applications 7
In Exercise 1.19, the mean and standard deviation of the amount of chloroform present in water sources were given to be 34 and 53, respectively. You argued that the amounts of chloroform could therefore not be normally distributed. Use Tchebysheffs theorem (Exercise 1.32) to describe the distribution