Statistics and Probability Answers

​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?

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?

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.

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 research company polled a random sample of 834 teens about Internet use. 43​% of those teens reported that they had misrepresented their age online to gain access to websites and online services.Calculate the standard error of p

A baseball player hit 5757 home runs in a season. Of the 5757 home​ runs, 1515 went to right​ field, 2121 went to right center​ field, 88 went to center​ field, 1111 went to left center​ field, and 22 went to left field.​ (a) What is the probability that a randomly selected home run was hit to leftleft ​field? (b) Was it unusual for this player to hit a home run to leftleft ​field?