A retail store is considering adding a new product line to its inventory. The store wants to know whether the new product line will be popular with customers. To determine this, they take a random sample of customers and ask if they would be interested in buying the new product line. Of the 125 people they asked, 70 were interested in this new product line. The manager is interested in creating a 90 % confidence interval regarding the population parameter.

In a statistics activity, students are asked to determine if there is a difference in the proportion of times that a spinning penny will land with tails up, and the proportion of times a spinning dime will land tails up. The students are instructed to spin the penny and the dime 30 times and record the number of times they land tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Based on the 98% confidence interval, (–0.36, 0.22), is there evidence of a difference in proportions of tails side up for a penny and a dime? There is convincing evidence because the two sample proportions are different. There is not convincing evidence because the interval contains 0. There is convincing evidence because the difference in the two sample proportions is –0.07. Since this is not 0, there is a difference in the true proportions of tails up for pennies and dimes. There is not convincing evidence because the interval contains both…

An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816 ). (c) The statistics teacher at the high school was concerned about the potential bias in the survey. To obtain a potentially less biased estimate of the proportion, the statistics teacher used an alternate method for collecting student responses. A random sample of 300 students was selected, and each student was given the following instructions on how to respond to the question. • In private, flip a fair coin. • If heads, you…

A recent Gallup Poll interviewed a random sample of 1523 adults. Of these, 868 bought a lottery ticket in the past year. The same Gallup Poll asked its 1523 adult respondents and also 501 teens (ages 13 to 17) whether they generally approved of legal gambling: 63% of adults and 52% of teens said yes. The margin of error for a 95% confidence statement about teens would be a. greater than for adults, because the teen sample is smaller.b. less than for adults, because the teen sample is smaller.c. less than for adults, because there are fewer teens in the population.d. the same as for adults, because they both come from the same sample survey.e. Can't say, because it depends on what percent of each population was in the sample.

Find the margin of error for the​ 99% confidence interval used to estimate the population proportion. In a clinical test with 1200 subjects, 35​% showed improvement from the treatment.

In a random sample of 250 high school students, it was found that 85.2% (213) of them later graduated. Find the 95% and 98% confidence interval for the true proportion of all high school students who graduate. Compare the two proportions.

An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816 ). (b) Given the method used by the environmental science teacher to collect the responses, explain how bias might have been introduced and describe how the bias might affect the point estimate of the proportion of all students at the school who would respond yes to the question.

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A simple random sample of 1000 people age 18 or over is taken in a large town. It turns out that 189 people in the sample are newspaper readers. Calculate a 95%-confidence interval for the percentage of people (age 18 and over) in that town who read newspapers.

Use the study below for Part A, Part B, and Part C. A soft drink company surveys 500 shoppers and finds that 61% of shoppers prefer diet soda to regular soda. Part A: With a confidence level of 90%, what is the margin of error? Show your work and round to the nearest hundredth.Part B: If the sample size would increase to 1,000 respondents while keeping the rest of the variables the same, what would happen to the margin of error?Part C: Support your answer to Part B by finding the margin of error if 1,000 shoppers were surveyed while keeping the rest of the variables the same. Show your