A poll reported that only 408 out of a total of 1549 adults in a particular region said they had a "great deal of confidence" or "quite a lot of confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Complete parts (a) through (d) below. a. Find a 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools, and interpret this interval. The 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ( (Round to three decimal places as needed.) Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to three decimal places as needed.) O A. We are O B. We are OC. There is a OD. There is a % confident that the every sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between | and % confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between and % chance that the sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between and % chance that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between | and b. Find an 80% confidence interval and interpret it. The 80% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ( (Round to three decimal places as needed.) Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to three decimal places as needed.) O A. There is a O B. There is a % chance that the sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between and % chance that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between | and OC. We are % confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between and O D. We are % confident that the every sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between and c. Find the width of each interval by subtracting the lower proportion from the upper proportion, and state which interval is wider. The width of the 95% confidence interval is (Round to three decimal places as needed.) and the width of the 80% confidence interval is The (1) interval is wider.

1. Construct a 95% confidence interval to estimate the proportion of Wingate male students that are left- handed. From previous class surveys 17 out of 126 male students were left-handed. Interpret your confidence interval. By interpretation, I mean something like what is contained in the class notes, which is "we are X% certain that the true proportion of ...". 2. Construct a 95% confidence interval to estimate the proportion of Wingate female students that are left-handed. From class surveys 15 out of 181 female students were left-handed. Interpret your confidence interval. 3. Does it appear that males and females have the same proportion of left-handed people? This will help you decide - if your confidence intervals from problems 1 and 2 do not overlap, you could conclude that the proportion of left-handed males does not equal the proportion of left-handed females. If they overlap, you could not rule out the possibility that the two proportions are equal.

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Answer part B

A national survey of 2500adult citizens of a nation found that 25​%dreaded​ Valentine's Day. The margin of error for the survey was 4.6percentage points with 85​% confidence. Explain what this means. Which statement below is the best​ explanation?   A. There is 85​% confidence that 25​% of the adult citizens of the nation dreaded​ Valentine's Day.   B. In 85​% of samples of adult citizens of the​ nation, the proportion that dreaded​ Valentine's Day is between 0.204 and 0.296.   C. There is 85​% confidence that the proportion of the adult citizens of the nation that dreaded​ Valentine's Day is between 0.204 and 0.296.   D. There is 80.4​% to 89.6​% confidence that 25​% of the adult citizens of the nation dreaded​ Valentine's Day.

Suppose you want to estimate the proportion of employed adults who would continue working if they won $10 million in the lottery. A previous study on the issue of how to sample proportion of 0.59. How many employed adults should be randomly sampled in order to get a 99% confidence interval with a width of 0.3?

According to a telephone survey of adults, 86% of homeowners said that owning a home was a good investment, this survey included 1450 homeowners. 1. Construct a 99% confidence interval for the corresponding population proportion.  2. Construct a 97% confidence interval for the corresponding population proportion.

You do a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 90% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data. (Give your answer rounded to the nearest 4 decimal places if necessary.) {7.8, 8.9, 9.5, 11.2, 11.5, 8.3, 11.8, 8.4, 8, 8.4, 10.1, 10.3} (?,? )

Part b ?

Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Construct a 95% confidence interval for the true mean or proportion. Round to the nearest hundredth (2 decimal places). (  ,  )