Question

According to a scientific survey, satisfaction with democracy (SWD) in the United Kingdom in 2015 approximates a Normal distribution, N ~ (6.25; 2.15). Data from the same survey but from 2018 shows the following distribution of SWD N ~ (4.96; 2.39). SWD is measured on a scale from 1 to 10, where 1 indicates the lowest satisfaction with democracy and 10 refers to the highest level of SWD. Answer the following questions:

1. What is the % of respondents whose satisfaction of democracy is less or equal than 4 with democracy in 2015? (5%)

2. What is the % of respondents whose satisfaction of democracy is less or equal than 4 with democracy with democracy in 2018? (5%)

3. Calculate the population mean of SWD for the 2015 and for the 2018 samples. To do so, estimate 95% confidence intervals and note that the size of the 2015 sample is 1,088 individuals and the size of the 2018 sample is 999 individuals. (10%)

4. Compare the values of the confidence intervals and explain whether SWD changed in the United Kingdom during this period of time (10%)

Answer 1