Questions: A state legislator wants to determine whether his voters' performance rating (0-100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year. Rating (last year) 75 80 75 74 88 79 53 63 69 78 Rating (this year) 85 69 54 63 63 91 58 52 89 72

Transcript text: A state legislator wants to determine whether his voters' performance rating ( $0-100$ ) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the $90 \%$ confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Rating (last year) & 75 & 80 & 75 & 74 & 88 & 79 & 53 & 63 & 69 & 78 \\ \hline Rating (this year) & 85 & 69 & 54 & 63 & 63 & 91 & 58 & 52 & 89 & 72 \\ \hline \end{tabular}