Question 1

A confidence interval for the population mean number of US states Americans have visited was found to be 11.9 to 12.3. 1) Find the midpoint of this confidence interval:

2) State the confidence interval in the form margin of error: ------ -----

Question 2

In a random sample of 368 people that were tested for the Norcovirus, it was found that 309 did not have the virus. Construct a 90% confidence interval to estimate the proportion of the population that does not have the Norcovirus. < Select an answer p p x s s < Do not round between steps. Round your answers to at least 3 decimal places.

Question 3

In a survey, 15 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $44 and standard deviation of $6. Construct a confidence interval at a 98% confidence level. Give your answers to one decimal place.

Question 4

If you want a poll to have a margin of error of 3.53%, how large will your sample have to be? Round your answer to the nearest whole number.

Question 5

If you want a poll to have a margin of error of 3.55%, how large will your sample have to be? Round your answer to the nearest whole number.

Question 6

If n = 520 and ^ (p-hat) = 0.3, construct a 90% confidence interval. Give your answers to three decimals ---- < p < -----

Question 7

Out of 300 people sampled, 114 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places --- < p <---

Question 8

You measure 47 randomly selected textbooks' weights, and find they have a mean weight of 52 ounces. Assume the population standard deviation is 13.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places ------ < < -------

Question 9

You measure 22 watermelons' weights, and find they have a mean weight of 70 ounces. Assume the population standard deviation is 2.3 ounces. Based on this, construct a 95% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places ------ ----- ounces

Question 10

If n=17, (x-bar)=47, and s=17, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. ------- < < ------

Question 11

In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $38 and standard deviation of $17. Construct a confidence interval at a 99% confidence level. Give your answers to one decimal place. ------- ---------

Question 12

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.025 margin of error at a 90% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.025 margin of error? Round your answerup to the nearest whole number.

n = households

b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of^=0.21. Using this new information.what sample size should you gather in order to obtain a 0.025 margin of error? Round your answerup to the nearest whole number.

n = households

Question 13

If you want a poll to have a margin of error of 2.35%, how large will your sample have to be? Round your answer to the nearest whole number. = people

Question 14

If you want a poll to have a margin of error of 2.79%, how large will your sample have to be? Round your answer to the nearest whole number. = people

Question 15

An urban economist wished to estimate the proportion of people living in Chicago who own the property they live in. What size sample should be obtained if she wishes to obtain an estimate with an error of 0.035 and 90% confidence level if

a) she uses a 2020 census estimate of =0.46 ? (Round your answer up to the nearest whole number.)

n = households

b) she uses no prior estimates? (Round your answer up to the nearest whole number.)

n = households

Question 16

Let's say we want to calculate the 90% confidence interval for a population proportion. Based on previous research, a reasonable guess for the population proportion is 28%. For this guess for the population proportion, find the necessary sample size to find a 90% confidence level with a margin of error of 3%: = Now, if you find yourself in a situation where you do not have a reasonable guess for the population proportion, then you can always use the worst-case scenario. It turns out, the largest sample size will be needed when the population proportion is 50%. Find the necessary sample size to find a 90% confidence level with a margin of error of 3% with =50%: =

Question 17

You work for a news organization, and you are asked to spearhead a political poll for a local election. After spending considerable time and resources making sure your sample was random and representative, you find that 56 out of the 100 respondents say they intend to vote for candidate Jones.

You make a 95% confidence interval and find that this sample size leads to [0.457, 0.659], which means that you are 95% confident that between 45.7% and 65.9% of voters intend to vote for candidate Jones.

Your boss laughs at you because this is completely useless information. Your boss orders you to increase your sample size (considerably.)

Choose a new, much higher sample size and compute a new confidence interval. Don't choose my sample size or someone else's. You can assume that the sample proportion will continue to be 56% for your new sample. (Round your number of respondents that intend to vote for candidate Jones to the nearest whole number, if applicable.)

Post your new confidence interval for your new sample size, and write at least one sentence on whether you think this Confidence Interval has any practical application. (Do you think your results on the estimate proportion of voters is useful and should be published?)

**For an example to question 17, I will choose a sample size of 659. That is my n.

56% of 659 is 369 (rounded to the nearest whole number.) That is my x.

My 95% confidence interval is [.521, .598] intend to vote for Candidate Jones, which means my 95% confident that between 52.1% and 59.8% of voters will vote for Candidate Jones.**

Please answer the question sequentially. Thank you.