Ten engineering schools in a country were surveyed. The sample contained 250 electrical engineers, 80 being women; 150 chemical engineers, 30 being women. Compute a 99% confidence interval for the difference between the proportions of women in these two fields of engineering. Is there a significant difference between the two proportions?[Hyperlinks]- Click here to view page 1 of the standard normal distribution table.- Click here to view page 2 of the standard normal distribution table.---Let $ p_1 $ be the population proportion of electrical engineers that are women in the schools that were surveyed, and let $ p_2 $ be the population proportion of chemical engineers that are women in the schools that were surveyed.The 99% confidence interval is $\text{[box]} < p_1 - p_2 < \text{[box]}$.(Round to three decimal places as needed.) ### Confidence Interval Calculation for MP3 Player TestingA manufacturer of MP3 players conducts a set of comprehensive tests on the electrical functions of its products. All MP3 players must pass all tests prior to being sold. In a random sample of 700 MP3 players, 28 failed one or more tests. Our goal is to find a 90% confidence interval for the proportion of MP3 players from the population that pass all tests.#### Resources- [Page 1 of the standard normal distribution table](#)- [Page 2 of the standard normal distribution table](#)---### Confidence Interval FormulaThe 90% confidence interval is given as:\[\text{ } < p < \text{ }\](Round to three decimal places as needed.)

“Since you have posted multiple questions, we will provide the solution only to the first question as per our Q&A guidelines. Please repost the remaining questions separately.”The sample size for the electrical engineers is n1=250The number of women in the total sample of electrical engineers is x1=80Let p^1 be the sample proportion of electrical engineers that are women, p^1=x1n1=0.32The sample size for the chemical engineers is n2=150The number of women in the total sample of chemical engineers is x2=30Let p^2 be the sample proportion of chemical engineers that are women, p^2=x2n2=0.2The defined confidence level is (1−α)=0.99Then the level of significance is α=0.01To find :The 99% confidence interval for the proportion of women in the two fields of engineering.The formula to compute the (1−α)%confidence interval for the difference in the proportion is given byTherefore the 99% confidence interval is, Since there is no 0 included in the confidence interval for (p1−p2), the difference between the two proportions is significant at a 0.01 level of significance.The 99% confidence interval is, Since there is no 0 included in the confidence interval for (p1−p2), the difference between the two proportions is significant at a 0.01 level of significance.