A sample survey asks a nationwide random sample of 2500 adults if they agree or disagree that "I like buying new clothes, but shopping is often frustrating and time-consuming." Suppose that 60% of all adults would agree if asked this question. (This is a problem involving confidence interval estimates for proportions.) a) What is the population mean of all possible sample proportions? (Explain/show how you obtain your answer.) b) What is the standard error of all possible sample proportions? (Explain/show how you obtain your answer.) c) What is the probability that the sample proportion who agree is at least 58%? (Explain/show how you obtain your answer.) d) Please fill in the blanks: 95% of the sample proportions symmetrically around the population proportion will have between ________% and ________% of the customers agree they like buying new clothes but shopping is often frustrating and time-consuming. (Explain/show how you obtain your answer.)
Added by Craig A.
Step 1
6. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Cheng Zhang and 89 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Surveys show that fewer people enjoy shopping in stores than in the past. A manager of a clothing store claims that 60% of all U.S. adults prefer shopping for clothes online rather than in a store. Suppose a random sample of 2500 U.S. adults were asked if they agreed or disagreed with the statement, "I prefer to shop for clothes online rather than in a store." Let p̂ be the proportion of people in the sample that prefer to shop for clothes online rather than in a store. (a) What is the shape, mean, and standard deviation of the sampling distribution of p̂? (b) Of the poll respondents, 63% agreed. Find the probability of obtaining a sample of 2500 U.S. adults in which 63% or greater prefer shopping for clothes online, assuming the manger's claim is true. (c) Based on your answer in part (b), do you have reason to doubt the manager's claim?
Thuc N.
Sample size for estimating the mean of a population does not depend on: a. Confidence level b. Sampling error c. Population size d. Sampling error and confidence level e. Variance of population If P(A and B) = P(A) * P(B), then A and B are: a. Dependent b. Collectively exhaustive c. Mutually exclusive and dependent d. Mutually exclusive e. Independent The sample size of a survey was 50. The variance of the population is unknown. The probability distribution that should be used to estimate the confidence interval of the mean of the population is: a. "t" distribution b. "Z" distribution c. Standard normal distribution d. Normal distribution e. "F" distribution The Prime Minister's car and other cars in the convoy are of the same brand, model, and color. This is done to: a. Increase mean b. Increase sampling error c. Increase median d. Increase variance e. Increase mode
Derrick D.
A simple random sample of size $n$ is drawn from a population whose population standard deviation, $\sigma,$ is known to be $3.8 .$ The sample mean, $\bar{x}$, is determined to be $59.2 .$ (a) Compute the $90 \%$ confidence interval about $\mu$ if the sample size, $n,$ is 45 (b) Compute the $90 \%$ confidence interval about $\mu$ if the sample size, $n,$ is $55 .$ How does increasing the sample size affect the margin of error, $E ?$ (c) Compute the $98 \%$ confidence interval about $\mu$ if the sample size, $n,$ is $45 .$ Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, $E ?$ (d) Can we compute a confidence interval about $\mu$ based on the information given if the sample size is $n=15 ?$ Why? If the sample size is $n=15,$ what must be true regarding the population from which the sample was drawn?
Estimating the Value of a Parameter Using Confidence Intervals
The Logic in Constructing Confidence Intervals about a Population Mean where the Population Standard Deviation Is Known
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD