A sample of n = 16 households was selected for a study of whether their property insurance premium has changed. Matched pairs {(Xj,Yj) : 1 j 16} were collected and processed. The X-value represented the premium paid in the past year, and Y was the projected premium for the next year. Sample summaries are shown below.

X = $2,300 and Y = $2,850

with the differences {Dj = Yj Xj : 1 j 16} that show the sample standard deviation S = $1,000 At the significance level = 0.01 = 1%, do you have sufficient evidence that the population average for insurance premium has increased?

1. Show the critical value and formulate the rejection rule

2. Evaluate test statistic

3. Finally, state your decision about the null hypothesis, whether it would be rejected

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