Construct a 90% confidence interval for the variance (standard deviation) of all voltages in the house. Procedure: Select an answer One mean Z procedure One proportion Z procedure One variance χ² procedure One mean T procedure Assumptions: (select everything that applies) The number of positive and negative responses are both greater than 10 Population standard deviation is unknown Simple random sample Sample size is greater than 30 Population standard deviation is known Normal population Unknown parameter: Select an answer p, population proportion σ², population variance μ, population mean Point estimate: Select an answer sample mean, x̄ sample variance, s² sample proportion, p̂ = (Round the answer to 3 decimal places) Confidence level % and α=α= , also α2=α2= , and 1−α2=1-α2= Critical values: (Round the answer to 3 decimal places) left= right= Margin of error (if applicable): (Round the answer to 3 decimal places) Lower bound: (Round the answer to 3 decimal places) Upper bound: (Round the answer to 3 decimal places) Confidence interval:(, ) Interpretation: We are % confident that the true population variance is between and . Based on the confidence interval, is it reasonable to believe that the population variance is less than 0.02? Explain. ? No Yes , because Select an answer a part or the entire interval is above the entire interval is above the entire interval is below a part or the entire interval is below 0.02.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The proper operation of typical home appliances requires voltage levels that do not vary much. Listed below are 14 voltage levels (in volts) at a random house on 14 different days.
| 120.2 | 120.1 | 119.9 | 119.7 | 119.9 |
| 120 | 120 | 120.1 | 119.8 | 120.1 |
| 120.3 | 120 | 120 | 120 |
The
Construct a 90% confidence interval for the variance (standard deviation) of all voltages in the house.
- Procedure: Select an answer One mean Z procedure One proportion Z procedure One variance χ² procedure One mean T procedure
- Assumptions: (select everything that applies)
- The number of positive and negative responses are both greater than 10
- Population standard deviation is unknown
- Simple random sample
- Sample size is greater than 30
- Population standard deviation is known
- Normal population
- Unknown parameter: Select an answer p, population proportion σ², population variance μ, population mean
- Point estimate: Select an answer sample mean, x̄ sample variance, s² sample proportion, p̂ = (Round the answer to 3 decimal places)
- Confidence level % and α=α= , also
- α2=α2= , and 1−α2=1-α2=
- Critical values: (Round the answer to 3 decimal places)
- left= right=
- Margin of error (if applicable): (Round the answer to 3 decimal places)
- Lower bound: (Round the answer to 3 decimal places)
- Upper bound: (Round the answer to 3 decimal places)
- Confidence interval:(, )
- Interpretation: We are % confident that the true population variance is between and .
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