Determine The Level Of Measurement For Voltage Measurements

Determine The Level Of Measurementvoltage Measurements From My House

Determine The level of measurement: Voltage measurements from my house _____________________ Book genre _____________________ Outside temperature in Silver Spring _____________________ Restaurant ratings on a scale of 0-5 stars _____________________ Determine type of sampling used: I collect data from this class _____________________ Data from every 4th patient in hospital _____________________ Data from 400 randomly selected students from those majoring in business, 763 randomly selected students from those majoring in education, and 392 randomly selected students from those majoring in criminal justice _________________ Data from 4230 adults after their phone numbers were randomly generated by computer ____________________ (2 points) The frequency distribution below shows the distribution for checkout time (in minutes) in Trader Joe’s grocery store between 8:00 and 9:00 AM on a Tuesday morning.

Checkout Time (in minutes) Frequency 1.0 - 1..0 - 2..0 - 3..0 - 4..0 - 5.9 2 Using the data above, answer the following questions. What percentage of the checkout times was at least 4 minutes? Calculate the mean of this frequency distribution. Calculate the standard deviation of this frequency distribution. Assume that the smallest observation in this dataset is 1.2 minutes.

Suppose this observation was incorrectly recorded as 0.12 instead of 1.2. What will happen to the mean and the median? Explain. Create a histogram (not a bar graph!) (2 points) I counted the number of words on each posting from my Class Announcements and found the following: What is the 5-number summary? Construct a boxplot.

Environmental scientists measured CO2 emissions of a sample of cars in tons. Is the value of 9.3 unusual? Base your answers on the standard deviation, which must be included in your answer. 7.1 7.4 7.9 6.5 7.2 8.2 9.3 My cousin was 38 when she retired from the military. Most people who retire have a mean age of 43.8 years.

The standard deviation is 8.9 years. What is the difference between my cousin’s age and the mean age? How many standard deviations is that (difference found in part a)? Convert my cousin’s age to a z-score If we consider “usual†age to be those that convert to a z score between -2 and +2, is my cousin’s age usual or unusual? An airline knows that the mean weight of all pieces of passengers’ luggage is 49.3 lb with a standard deviation of 8.4 lb. What is the probability that the weight of 66 bags in a cargo hold is more than the plane’s total weight capacity of 3,500 lb?

Paper For Above instruction

The assignment involves multiple statistical tasks, including identifying levels of measurement, types of sampling, analyzing and interpretating frequency distribution and data, and applying statistical concepts such as mean, standard deviation, Z-scores, and probability. This comprehensive analysis provides insights into different data types, sampling methods, descriptive statistics, and probability theory, reinforced through specific examples and calculations.

Part 1: Level of Measurement

Voltage measurements from a residential power source are considered ratio data. They have a true zero point, equal intervals, and allow for meaningful ratio comparisons. For instance, a voltage reading of 0 volts indicates no electrical potential, and a reading of 120 volts is twice as high as 60 volts, exemplifying ratio measurement.

The book genre is an example of nominal measurement. Genres such as fiction, non-fiction, mystery, or romance are categories without inherent order or quantitative value.

Outside temperature in Silver Spring is an example of interval data. Temperatures are measured on a scale where differences are meaningful, but there is no true zero point (e.g., 0°C does not mean ‘no temperature’), making it an interval measurement. Celsius and Fahrenheit are typical interval scales.

Restaurant ratings on a scale of 0-5 stars are ordinal data because they signify order (more stars imply better ratings), but the intervals between ratings are not necessarily equal or meaningful in a quantitative way.

Part 2: Types of Sampling

Data collected from this class appears to be a convenience sample, as it is gathered from students readily available and easily accessible to the researcher.

Data from every 4th patient in a hospital exemplifies systematic sampling, where a starting point is chosen, and every nth individual (here, every 4th patient) is selected.

Data from 400 randomly selected students from majors in business, 763 in education, and 392 in criminal justice involves stratified random sampling. The population is divided into strata (majors), and random samples are taken from each, ensuring representation across groups.

Data from 4230 adults with phone numbers generated randomly by a computer represents simple random sampling, where each individual has an equal probability of being selected, ensuring a representative sample.

Part 3: Analysis of Frequency Distribution

The frequency distribution for checkout times illustrates how long customers spend in the checkout lane. To determine the percentage of times at least 4 minutes, sum the frequencies of time intervals of 4 and above, then recalculate as a percentage of total observations.

• Suppose frequencies are distributed as follows:
• 1.0-2.0 min: 10
• 2.0-3.0 min: 15
• 3.0-4.0 min: 20
• 4.0-5.0 min: 25
• 5.0-5.9 min: 30

Percentage of checkout times at least 4 minutes = [(25 + 30) / total] 100%. The total is 10 + 15 + 20 + 25 + 30 = 100, so percentage = (55/100) 100% = 55%.

Calculating the mean involves multiplying each midpoint of intervals by their frequency, summing these products, and dividing by the total number of observations. For approximate midpoints: 1.5, 2.5, 3.5, 4.5, 5.45 minutes; the mean is the sum of (midpoint × frequency) divided by total observations.

To calculate the standard deviation, find the squared deviations from the mean, multiply by frequencies, sum, and then divide by total, finally taking the square root. This provides a measure of data dispersion.

If the smallest observation was incorrectly recorded as 0.12 instead of 1.2, the mean would decrease because 0.12 is less than 1.2, pulling the average downward. The median might also shift depending on data distribution, but typically, the median is less affected by an extreme small value compared to the mean.

Creating a histogram (not a bar chart) involves plotting the frequency of checkout times on the y-axis against time intervals on the x-axis with continuous bars, illustrating the distribution’s shape.

Part 4: Five-Number Summary and Boxplot

The number of words per class announcement posting could be summarized: minimum, first quartile, median, third quartile, maximum. For example, if the counts are 50, 75, 100, 125, and 150 words, the five-number summary is as above. A boxplot can then be constructed to visualize data spread and identify outliers.

Part 5: Identifying Unusual Values Using Standard Deviation

The CO2 emission measurement of 9.3 tons can be assessed for unusualness by calculating its z-score relative to the mean and standard deviation of the data (mean 7.1, SD 0.9).

Z = (9.3 - 7.1) / 0.9 ≈ 2.44, indicating that 9.3 is more than 2 standard deviations above the mean, making it a likely outlier or unusual value.

For the retired military cousin aged 38, with a mean age of 43.8 years and SD of 8.9 years, the difference is 43.8 - 38 = 5.8 years. The number of standard deviations is 5.8 / 8.9 ≈ 0.65, well within the range of typical variation. The z-score is (38 - 43.8) / 8.9 ≈ -0.65. Since this z-score falls between -2 and 2, her age is considered usual.

Regarding the airline luggage weights, the mean is 49.3 lb with SD 8.4 lb. The total expected weight for 66 bags is 66 × 49.3 = 3253.8 lb. The standard deviation of the sum is √66 × 8.4 ≈ 21.57 lb. The probability that total weight exceeds 3500 lb is calculated with z = (3500 - 3253.8) / 21.57 ≈ 11.45, which corresponds to virtually zero probability based on the normal distribution. Hence, the likelihood that 66 bags collectively exceed the cargo weight limit is extremely low.

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