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Wildlife biologists inspect 152 deer taken by hunters and find 24 of them carrying ticks that test positive for Lyme disease.
a) Create a 90% confidence interval for the percentage of deer that may carry such ticks.
a) Create a 90% confidence interval for the percentage of deer that may carry such ticks.
It's believed that as many as 22% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.
a) How many of this younger age group must we survey in order to estimate the proportion of non-grads to within 10% with 90% confidence?
a) How many of this younger age group must we survey in order to estimate the proportion of non-grads to within 10% with 90% confidence?
It's believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 2%?
An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 5% and 90% confidence. To gauge the size of the problem, the agency first picks 80 cars and finds 16 with faulty emissions systems. How many should be sampled for a full investigation?
A newspaper reports that the governor's approval rating stands at 54%. The article adds that the poll is based on a random sample of 4134 adults and has a margin of error of 2%. What level of confidence did the pollsters use?
Of 560 broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause food-borne illnesses, 65% were infected with a particular bacterium.
a) Construct a 90% confidence interval.
b) Explain what your confidence interval says about chicken sold in the country.
c) A government spokesperson claimed that the sample size was too small, relative to the billions of chickens slaughtered each year, to generalize. Is this criticism valid?
a) Construct a 90% confidence interval.
b) Explain what your confidence interval says about chicken sold in the country.
c) A government spokesperson claimed that the sample size was too small, relative to the billions of chickens slaughtered each year, to generalize. Is this criticism valid?
The weight of potato chips in a large-size bag is stated to be 16 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 16.3 ounces and a standard deviation of 0.19 ounces.
a) What fraction of all bags sold are underweight?
b) Some of the chips are sold in "bargain packs" of 3 bags. What's the probability that none of the 3 is underweight?
c) What's the probability that the mean weight of the 3 bags is below the stated amount?
d) What's the probability that the mean weight of a 24-bag case of potato chips is below 16 ounces?
a) What fraction of all bags sold are underweight?
b) Some of the chips are sold in "bargain packs" of 3 bags. What's the probability that none of the 3 is underweight?
c) What's the probability that the mean weight of the 3 bags is below the stated amount?
d) What's the probability that the mean weight of a 24-bag case of potato chips is below 16 ounces?
A college's data about the incoming freshmen indicates that the mean of their high school GPAs was 3.2, with a standard deviation of 0.20; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of 25. What might the mean GPA of one of these seminar groups be? Describe the appropriate sampling distribution model, including shape, center, and spread, with attention to assumptions and conditions. Make a sketch using the 68-95-99.7 Rule. Describe the appropriate sampling distribution model, including shape, center, and spread.
Just before a referendum on a school budget, a local newspaper polls 373 voters to predict whether the budget will pass. Suppose the budget has the support of 53% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
After the political ad campaign, pollsters check the mayor's negatives. They test the hypothesis that the ads produced no change against the alternative that the negatives are now below 65% and find a P-value of 0.483. Which conclusion is appropriate? Explain.
