Posted: September 16th, 2017

STATS Problems with Solution,

2. Construct a histogram that corresponds to the frequency distribution from exercise 1. Applying a very strict interpretation of the requirements for a normal distribution, does the histogram suggest that the data are from the population having a normal distribution? why or why not?

(this is exercise 1 ) 1. Complete the frequency distribution of the 20 brain volumes (cu. cm.) listed below (from data set 6 in Appendix B)
1005 963 1035 1027 1281 1272 1051 1079 1034 1070
1173 1079 1067 1104 1347 1439 1029 1100 1204 1160

4. listed below are the first eight IQ scores from data set 6 in appendix B. construct a stem plot of these eight values. is this data set large enough to reveal the true nature of the distribution of the IQ scores for the population from which the sample is obtained?

96, 89, 87, 87, 101, 103, 103, 96

5. listed below are the amounts (million metric tons) of carbon monoxide emissions in the United States for each year of a recent ten-year period. the data are listed in order. construct the graph that is most appropriate for these data. what type of graph is best? what does the graph suggest?

5638, 5708, 5893, 5807, 5881, 5939, 6024, 6032, 5946, 6022

6. Exercise 5 lists the amounts of carbon monoxide emissions, and listed below are the amounts (million metric tons) of nitrous oxide emissions in the United States for the same 10-year period in exercise 5. What graph is best for exploring the relationship between carbon monoxide emissions and nitrous oxide emissions? Construct that graph. Does the graph suggest that there is a relationship between carbon monoxide emissions and nitrous oxide emissions?
351 349 345 339 335 335 362 371 376 384

2. Using the sample data from Exercise 1, find the z score corresponding to the eye height of 1642 mm. Is that height unusual? Why or why not?
3. Using the same standing height listed in Exercise 1, construct a boxplot and include the value of the number 5-number summary. Does the boxplot indicate that the data are from a population with a normal (bell shaped) distribution? Explain.

5. The body mass indices of a sample of males have a mean of 26.601 and a standard deviation of 5.359. The body mass indices of a sample of females have a mean of 28.441 and a standard deviation of 7.394. When considered among members of the same gender, who has the relatively larger BMI: a male with a BMI of 28.00 or a female with a BMI of 29.00? Why?
6. Consider the price of regular movie tickets (not 3-D and not discounted for children or seniors).
Estimate the mean price.
Use the range rule of thumb to make a rough estimate of the standard deviation of the price.

use data from table express all probabilities as decimal numbers.

[guilty plea ][ plea of not guilty]
sentenced to prison – 392 58
not sentenced to prison – 564 14

5. if 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a plea of guilty.
6. if 2 different study subjects are randomly selected, find the probability that they both were sent to prison
7. if 2 different study subjects are randomly selected, find the probability that they both entered pleas of not guilty.
assume that 40% of the population has brown eyes 1-4

if six people are randomly selected, find the probability that none of them has brown eyes.
3. Groups of 600 people are randomly selected. Find the mean and standard deviation for the numbers of people with brown eyes in such groups, then use the range rule of thumb to identify the range of usual values for those with brown eyes. For such a group of 600 randomly selected people, is 200 with brown eyes unusually low or high?

4. when randomly selecting 600 people, the probability of exactly 239 people with brown eyes is p(239)=0.331. Also, p(239 or fewer) =0.484. which of those two probabilities is relevant for determining whether 239 is an unusually low number of people with brown eyes? is 239 an unusually low number of people with brown eyes?

x- o, 1, 2, 3, 4 p(x) 0.674, 0.280, 0.044, 0.003,0+
5. does the table describe probability distribution? why or why not?
6. find the mean and standard deviation for the random variable x. use the range rule of thumb to identify the range of usual values for the numbers of males with tinnitus among four randomly selected males. is it unusual to get three males with tinnitus among four randomly selected males.

duration -240, 120, 178, 234, 235, 269, 255, 220
height- 140, 110, 125, 120, 140, 120, 125, 150
interval before- 98, 90, 92, 98, 93, 105, 81, 108
interval after- 92, 65, 72, 94, 83, 94, 101, 97
(pearson correlation of duration and after= 0.926
p-value =0.001
the regression equation is after = 34.8 + 0.234 duration)

2. refer to the table of data given in exercise 1 and use the heights and interval after times.
construct a scatterplot. what does the scattrplot suggest about a linear correlation between heights of eruptions and interval after times?
find the value of the linear correlation coefficient and determine whether there is sufficient evidence to support a claim of a linear correlation between heights of eruptions and interval aftertimes.
letting y represent the interval after time and letting x represent height, find the regression equation.
based on the given sample data, what is the best predicted interval after time for an eruption with a height of 100 ft.

2. when certain quantities are measured, the last digits tend to be uniformly distributed, but if they are estimated or reported, the last digits tend to have disproportionately more 0s or 5s. if we use the last digits (decimal portion) of the 80 weights in Data set 1 from appendix B, we get the frequency counts in table below. use a 0.05 significance level to test the claim that the last digits of 1, 2, …, 9 occur with the same frequency. does it appear that the weights were obtained through measurements?
last digit: 1,2,3,4,5,6,7,8,9
frequency: 6,7,4,11, 10, 8, 5, 9, 10, 10

4. a study was conducted of 531 persons injured in bicycle crashes, and randomly selected sample results are summarized in the accompanying table. The TI-83/84 Plus calculator results also are shown. At the 0.05 significant level, test the claim that wearing a helmet has no effect on whether facial injuries are received. Based on these results, does a helmet seem to be effective in helping to prevent facial injuries in a crash?

{fatal injuries received} helmet worn- 30 no helmet 182
{all injuries nonfacial} helmet worn- 83 no helmet 236

 

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