Please type up answers and show work. Thank you!

1.Answer the following questions in words, giving examples or equations to explain your answers:

a.Are the requirements for a z and a t test for the mean the same?

b.What does the p-value of a hypothesis test represent?

c.What do we mean when we say a statistical test is significant?

d.Can the conclusions of a one-tailed and a two-tailed test be different?

e.What is the difference between a dependent and an independent two samples t-test for the comparison of means?

2.In California, Senate Bill 1368 limits the amount of CO2 that power plants can emit.The standard is 1100 lbs of CO2 per Megawatt (MW) of electrical power that is generated (on average).You suspect that the power plant exceeds the standard. (Data attached below.)

a.What is the null hypothesis?

b.What is the alternative hypothesis?

c.Explain real-world consequences of making a Type 1 error.

d.Explain real-world consequences of making a Type 2 error.

e.Is a hypothesis test for this case left tailed, right tailed, or two tailed?

f.Do the data supply evidence of the power plant exceeding the pollution standard?

Data:

CO2 Emissions from a power plant (lb CO2/MW) 712 1046 912 987 1018 1059 1274 941 1124 1080 842 1093 

3. You want to compare the air quality index during the month of December for an area with a dense network of highways, and an area away from the highway system. You find data from the two areas for each day of December, given in the data attached below. Does the data indicate that areas near highways are more heavily impacted by air pollution compared (have a higher AQI) than areas away from highways? Test the hypothesis at the 95% level.In your answer, include a graph comparing the average AQI of the two areas.(Data attached below.)

Data:

Date Area Daily_AQI 1-Dec near-highway 86 2-Dec near-highway 117 3-Dec near-highway 79 4-Dec near-highway 89 5-Dec near-highway 70 6-Dec near-highway 90 7-Dec near-highway 122 8-Dec near-highway 66 9-Dec near-highway 85 10-Dec near-highway 70 11-Dec near-highway 80 12-Dec near-highway 134 13-Dec near-highway 55 14-Dec near-highway 68 15-Dec near-highway 51 16-Dec near-highway 79 17-Dec near-highway 137 18-Dec near-highway 110 19-Dec near-highway 32 20-Dec near-highway 62 21-Dec near-highway 106 22-Dec near-highway 52 23-Dec near-highway 103 24-Dec near-highway 54 25-Dec near-highway 97 26-Dec near-highway 102 27-Dec near-highway 85 28-Dec near-highway 109 29-Dec near-highway 91 30-Dec near-highway 105 31-Dec near-highway 131 1-Dec control 40 2-Dec control 44 3-Dec control 126 4-Dec control 59 5-Dec control 83 6-Dec control 83 7-Dec control 118 8-Dec control 26 9-Dec control 127 10-Dec control 42 11-Dec control 6 12-Dec control 7 13-Dec control 37 14-Dec control 32 15-Dec control 97 16-Dec control 29 17-Dec control 52 18-Dec control 24 19-Dec control 103 20-Dec control 51 21-Dec control 43 22-Dec control 56 23-Dec control 24 24-Dec control 38 25-Dec control 40 26-Dec control 45 27-Dec control 44 28-Dec control 29 29-Dec control 87 30-Dec control 66 31-Dec control 69