Confidence Intervals for p
Compute the critical value for a Z distribution at 99%.
2.33
What is the critical value t for constructing a 95% confidence interval for a mean with a sample size of 9?
2.306
A government report on standard of living says that family incomes nationwide are skewed to the right, with a mean of $33,400. A sample of randomly chosen families produced a 90% confidence interval for the local mean family income of (32882, 44761). Does this interval provide evidence that family incomes are unusually high here? Explain briefly.
No; this county’s mean could be the same as the national mean because 33400 is in the confidence interval.
What country lies directly south of Detroit?
Canada
A school administrator wants to know what proportion of teachers in their state have a Master's degree. The administrator takes an SRS of 30 teachers from a statewide database containing every teacher, and they find 21 teachers in the sample have a Master's degree. The administrator wants to use this data to construct a one-sample z interval for a proportion.
Which conditions for constructing this confidence interval did their sample meet?
Randomness and Independence
(Normality fails as there are only 9 "failures")
Give the 3 cases in which the normality condition can be met when working with means (quantitative data).
1) parent population is normal
2) The sample size is large (30 or more)
3) The sample data shows no strong skew or outliers
A statistic is said to be unbiased if (which of the following)
a)the mean of its sampling distribution is equal to the true value of the parameter being estimated
b) both person who calculated the statistic and the subjects whose responses make up the statistic were truthful
c)it is used for honest purposes only
d) none of the above.
a)the mean of its sampling distribution is equal to the true value of the parameter being estimated
What element's chemical symbol is "Pb"?
Lead
From time to time police set up roadblocks to check cars to see if the safety inspection is up to date. At one such roadblock they issued tickets for expired inspection stickers to 22 of 628 cars they stopped. Based on the results at this roadblock, construct a 95% confidence interval for the proportion of autos in that region whose safety inspections have expired.
(.02, .05)
A quality control expert at a pretzel factory took a random sample of 10 bags from a production run of over 500 bags and measured the amount of pretzels in each bag in the sample. The sample data were roughly symmetric with a mean of 450g, and a standard deviation of 15g.
Based on this sample, find a 90% CI for the mean amount of pretzels per bag (in grams) in this production run?
(441.3, 458.7)
Name the 3 conditions for calculating intervals and match it to the part of the sampling distribution that it relates to (shape, center, or spread).
Randomness - center (mean)
Independence - spread (standard deviation)
Normality - shape
What is the world's highest waterfall?
Angel Falls (Venezuela)
From time to time police set up roadblocks to check cars to see if the safety inspection is up to date. At one such roadblock they issued tickets for expired inspection stickers to 3% of cars they stopped. How many cars should they stop if they want to have a 95% confidence interval with a margin of error of 1%?
1118 cars
Nadia wants to estimate the mean driving range for her company's new electric vehicle. She'll sample vehicles and measure each of their driving ranges to construct a confidence interval for the mean driving range. She wants the margin of error to be no more than 10 kilometers at 90% confidence. A pilot study suggests that the driving ranges for this type of vehicle have a standard deviation of 15 kilometers.
Find the smallest approximate sample size required to obtain the desired margin of error.
7 vehicles
A baseball coach was curious about the true mean speed of fastball pitches in his league. The coach recorded the speed in miles per hour of each fastball in a random sample of 100 pitches and constructed a 95% confidence interval for the mean speed. The resulting interval was (78, 84).
Give the correct interpretation of the interval (78, 84).
We're 95% confident that the interval (78, 84) captured the true mean pitch speed.
Which 1951 Tony winner for Best Musical had its music and lyrics written by Frank Loesser and included such characters as Nathan Detroit, Miss Adelaide, and Sky Masterson?
Guys and Dolls
A newspaper article reported that a poll based on a sample of 800 voters showed the President’s job approval rating stood at 62%. They claimed a margin of error of ± 3%. What level of confidence were the pollsters using?
92% Confidence
A zoologist was interested in the average annual growth rate of Polar Bears. A sampling of 14 random bears found a mean growth rate of 3.4 feet with a standard deviation of 0.78 feet. The confidence interval estimated the true mean growth rate is most likely somewhere between 3.0531 and 3.7469. The given interval had what level of confidence?
88%
A political pollster plans to ask a random sample of 500 voters whether or not they support the incumbent candidate. The pollster will take the results of the sample and construct a 90% confidence interval for the true proportion of all voters who support the candidate.
Give the correct interpretation of the 90% confidence level?
If the pollster repeats this process many times, then about 90% of the intervals produced will capture the true proportion of voters who support the candidate.
Named after a 19th-century British surgeon and anatomist, the Bowman's capsule is located in which organ's of the human body?
Kidneys