You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 371 randomly selected caterpillars observed, 49 lived to become butterflies. Round answers to 4 decimal places where possible. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between ____ and ____  If many groups of 371 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About _____ percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about ____ percent will not contain the true population proportion.

A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table. Student   Test Grade 1 Test Grade 21 42 812 51 743 88 624 99 575 54 726 66 737 87 638 99 579 97 5810 89 6311 42 7712 71 6313 96 5514 56 7615 75 6916 57 7017 62 7518 89 6319 50 7220 56 7221 89 57Step 1 of 2 : Using statistical software, estimate the parameters of the modelSecond Test Grade=β0+β1(First Test Grade)+εi.Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

Section 6.3: Confidence Interval for a Difference in Proportions Example 3: Mobile Connections to Libraries In a random sample of 2,252 Americans age 16 and older, 11% of the 1,059 men and 16% of the 1,193 women said they have accessed library services via a mobile device. Find a 95% confidence interval for the difference in proportion accessing libraries via mobile devices, between men and women.

The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratios†. 11 35 19 13 15 21 40 18 60 72 9 20 29 53 16 26 21 14 21 27 10 12 47 14 33 14 18 17 20 19 13 25 23 27 5 16 8 49 44 20 27 8 19 12 31 67 51 26 19 18 32   (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.)   x =   s =     (b) Find a 90% confidence interval for the P/E population mean ? of all large U.S. companies. (Round your answers to one decimal place.)   lower limit       upper limit         (c) Find a 99% confidence interval for the P/E population mean ? of all large U.S.…