1.)

A city is considering mandating a complete switch to non-fossil fuel vehicles by year 2030. For the mandate to be successful, city planners launch a broad education campaign to inform the public about the benefits of the switch and about the incentives being given for people to only purchase electric vehicles going forward. The officials will go forward with the mandate vote only if at least 60% of the population are in favor of the new mandate.

To assess the population's interest in the mandate, surveys are administered to a sample of 600 people to ask whether people are favorable to the new mandate. The survey indicated that of the 600 people, 384 responded that they would definitely support the new mandate.

Compute a 95% confidence interval for the proportion of people supporting the new mandate.Based on this information, should the officials proceed with the mandate vote? (Data attached below.)

Please type up, show, and explain all work with equations. Thank you.

Total survey responses

600

Responses in favor

384

2.)

The department of energy wants to assess whether the energy generated by an existing windfarm suffices to meet the needs of an expanding urban center or whether additional power generation is necessary. Variable winds result in varying amounts of energy generation from the windfarm. If the windfarm's mean weekly energy generation is less than 6 MWh, then additional power generation capacity will need to be built. Data are collected weekly over the course of one year to assess whether the city needs to expand their energy infrastructure. (Data attached below.)

Use a confidence interval approach to evaluate this problem with95% confidence.

For the Question Above, please also complete:

A. What might the real-world consequences be of making aType Ierror in this case?

B. What might the real-world consequences be of making aType IIerror in this case?

Please type up, show, and explain all work with equations. Thank you.

Date Total weekly energy generated (MWh) 1-Jan 8.6 8-Jan 4.8 15-Jan 3.1 22-Jan 2.9 29-Jan 6.4 5-Feb 6.1 12-Feb 5 19-Feb 3.4 26-Feb 5.5 4-Mar 6.6 11-Mar 8.3 18-Mar 5.4 25-Mar 4.2 1-Apr 4.5 8-Apr 7.1 15-Apr 7.5 22-Apr 5 29-Apr 7 6-May 7.6 13-May 3.9 20-May 8.8 27-May 5.1 3-Jun 7.2 10-Jun 2.5 17-Jun 4.9 24-Jun 8.4 1-Jul 5.1 8-Jul 8.1 15-Jul 8.5 22-Jul 3.4 29-Jul 5.1 5-Aug 8.1 12-Aug 5.6 19-Aug 5.4 26-Aug 3.4 2-Sep 3.5 9-Sep 7.2 16-Sep 5.2 23-Sep 4.2 30-Sep 5.6 7-Oct 2.9 14-Oct 5.5 21-Oct 7.4 28-Oct 8.3 4-Nov 5 11-Nov 4.8 18-Nov 6.3 25-Nov 3.9 2-Dec 4.6 9-Dec 6.1 16-Dec 7.4 23-Dec 6.3 30-Dec 7.2