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Ott and Longnecker - Intro to Statistical Methods (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 2 / 29

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving...  ()

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1. 2/4 points  |  Previous Answers OLIntroStat6 3.E.004. My Notes
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The regulations of the board of health in a particular state specify that the fluoride level must not exceed 1.5 parts per million (ppm). The 25 measurements given here represent the fluoride levels for a sample of 25 days. Although fluoride levels are measured more than once per day, these data represent the early morning readings for the 25 days sampled.
.75 .86 .84 .85 .97
.94 .89 .84 .83 .89
.88 .78 .77 .76 .82
.72 .92 1.05 .94 .83
.81 .85 .97 .93 .79
(a) Determine the range of the measurements.
Correct: Your answer is correct.
(b) Dividing the range by 7, the number of subintervals selected, and rounding, we have a class interval width of .05. Use .705 as the lower limit of the first interval. Compute relative frequencies for each class interval and construct a relative frequency histogram. Note that if you create frequency and relative frequency histograms for these data they have the same shape.

Correct: Your answer is correct.

(c) If one of these 25 days were selected at random, what would be the chance (probability) that the fluoride reading would be greater than .90 ppm?
Incorrect: Your answer is incorrect.

Guess (predict) what percentage of days in the coming year will have a fluoride reading greater than .90 ppm.
Incorrect: Your answer is incorrect. %
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2. –/4 points OLIntroStat6 3.E.016. My Notes
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Refer to the data shown below.
55 85 90 50 110 115 75 85 8 23
70 65 50 60 90 90 55 70 5 31

Replace 110 and 115 with 345 and 467, respectively.
55 85 90 50 345 467 75 85 8 23
70 65 50 60 90 90 55 70 5 31

Compute the mean, median, and mode on the new data.
mean
median
mode

Discuss the impact of these extreme measurements, 345 and 467, on the three measures of central tendency.

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3. –/4 points OLIntroStat6 4.E.065. My Notes
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Let y be a normal random variable with μ = 500 and σ = 100. Find the following probabilities:
(a)    P(500 < y < 645)


(b)    P(y > 645)


(c)    P(305 < y < 645)


(d)    k such that P(500 − k < y < 500 + k) = .60
k =
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4. –/6 points OLIntroStat6 5.E.077. My Notes
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The recipe for producing a high-quality cement specifies that the required percentage of SiO2 is 6.2%. A quality control engineer evaluates this specification weekly by randomly selecting samples from n = 20 batches on a daily basis. On a given day, she obtained the following values:
1.70 9.86 5.44 4.28 4.59 8.76 9.16 6.28 3.83 3.17
5.98 2.77 3.59 3.17 8.46 7.76 5.55 5.95 9.56 3.58
(a) Estimate the mean percentage of SiO2 using a 95% confidence interval.
( , )

(b) Evaluate whether the percentage of SiO2 is different from the value specified in the recipe using an α = .05 test of hypothesis.
t =
p-value =
    

(c) Use the following plot to determine if the procedures you used in parts (a) and (b) were valid.

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5. –/11 points OLIntroStat6 6.E.025. My Notes
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PCBs have been in use since 1929, mainly in the electrical industry, but it was not until the 1960s that they were found to be a major environmental contaminant. In the paper "The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data,"† researchers report on the following study. Thirteen study sites from the five Great Lakes were selected. At each site, 9 to 13 herring gull eggs were collected randomly each year for several years. Following collection, the PCB content was determined. The mean PCB content at each site is reported in the following table for the years 1982 and 1996.
Site
Year 1 2 3 4 5 6 7 8 9 10 11 12 13
1982 61.48 64.47 45.50 59.70 58.81 75.86 71.57 38.06 30.51 39.70 29.78 66.89 63.93
1996 13.99 18.26 11.28 10.02 21.00 17.36 28.20 7.30 12.80 9.41 12.63 16.83 22.74
A potential criticism of analyzing these data as if they were two independent samples is that the measurements taken in 1996 were taken at the same site as the measurements taken in 1982. Thus, there is the possibility that there will be a strong positive correlation between the pair of observations at each site.
(a) Plot the pairs of observations in a scatterplot with the 1982 values on the horizontal axis and the 1996 values on the vertical axis.
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Does there appear to be a positive correlation between the pairs of measurements?
    

(b) Compute the correlation coefficient between the pair of observations.
r =

Does this value confirm your observations from the scatterplot?
    

(c) Answer the following questions using a paired data analysis.
(i) Legislation was passed in the 1970s restricting the production and use of PCBs. Thus, the active input of PCBs from current local sources has been severely curtailed. Do the data provide evidence that there has been a significant decrease in the mean PCB content of herring gull eggs? (Use α = .05, and let d = 1996 − 1982.)
t =
tα =
p-value =
    

(ii) Estimate the size of the decrease in mean PCB content from 1982 to 1996, using a 95% confidence interval.
( , )
Are your conclusions different from the conclusions you reached treating the data as two independent samples?
    
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