Critical Values
What does sigma represent when solving for confidence intervals?
population standard deviation
In a recent study of 75 people, 41 said they were dissatisfied with their community’s snow removal service. Find the 95% confidence interval of the true proportion of individuals who are dissatisfied with their community’s snow removal service
What is (.434,.659)
The number of unhealthy days based on the AQI (Air Quality Index) for a random sample of metropolitan areas is shown. Construct a 98% confidence interval based on the data. 61 12 6 40 27 38 93 5 13 40
What is (8.8, 58.195)
When should the t distribution be used? Two things must be met.
Its a mean problem, unknown pop sd
Why do we use t* instead of z* for CI of means?
Because we don't usually know the population standard deviation.
Find the p and q value: 93%
p=.93, q=.07
A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. Find the 90% confidence interval of the true mean
What is (3837.6,4136.4)
What is meant by the 95% confidence level of the mean?
What is 95% of the intervals made the same way will contain the true mean.
Which is wider? 99% or 95% confidence?
99% Confidence
Find the critical value when using a 94% confidence interval
What is 1.88
In a survey of 1004 individuals, 442 felt that President George W. Bush spent too much time away from Washington. Find a 95% confidence interval for the true population proportion.
What is (.409,.471)
A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Find the 99% confidence interval of the mean.
What is (13.6, 16.44)
True or false: to determine the sample size needed to estimate a parameter, you must know the margin of error of the estimate.
What is true
Conditions for Conf. Int for proportions.
Random/Independence/10%Condition
Normal Condition np and nq > 10
A federal report stated that 88% of children under age 18 were covered by health insurance in 2000. How large a sample is needed to estimate the true proportion of covered children with 90% confidence with a confidence interval 0.05 wide?
What is 455
The numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrollment under 12,000 students are shown below. Use these data to estimate the mean number of faculty at all state-controlled colleges and universities with enrollment under 12,000 with 92% confidence. 211 384 396 211 224 337 395 121 356 621 367 408 515 280 289 180 431 176 318 836 203 374 224 121 412 134 539 471 638 425 159 324
What is (293.42, 399.08)
If the sample size increases, what will happen to the size of the margin of error.
What is it will decrease.
Conditions for Conf. Int Means
Random/Independence/10% Condition
Normal:
Population is Normal
CLT n>30
Graph shows data is nearly normal
A U.S. Travel Data Center’s survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations.
What is (0.395, .445)
The national average for the number of students per teacher for all U.S. public schools in 15.9. A random sample of 12 school districts from a moderately populated area showed that the mean number of students per teacher was 19.2 with a variance of 4.41. Estimate the true mean number of students per teacher with 95% confidence
What is (17.87, 20.534)
If a 95% Confidence interval for proportions is (.12, .14), interpret that.
We are 95% confident that the true proportion will be between .12 and .14
If we want to keep the same confidence level but reduce our margin of error what can we do?
Increase our sample size (n)