Question: A study was conducted to measure the differences in total monthly exercise time in December 2021 and January 2022 for 10 subjects. The purpose of

  1. A study was conducted to measure the differences in total monthly exercise time in December 2021 and January 2022 for 10 subjects. The purpose of this study was to test the claim that New Year's resolutions do not impact exercise time. The results of the study are shown below. Construct a 95% confidence interval for the mean of the differences and choose the appropriate interpretation.

1 2 3 4 5 6 7 8 9 10
December 2021 360 180 500 120 960 0 1200 450 120 750
January 2022 400 170 450 120 1000 30 1680 400 120 700

  1. Using the 95% confidence interval (-78.65 to -7.35), we reject the null hypothesis and conclude there is sufficient evidence that New Year's resolutions do impact exercise time.
  2. Using the 95% confidence interval (-78.65 to -7.35), we fail to reject the null hypothesis and conclude is sufficient evidence to warrant rejection of the claim that New Year's resolutions do not impact exercise time.
  3. Using the 95% confidence interval (-155.75 to 69.75), we reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that New Year's resolutions do not impact exercise time.
  4. Using the 95% confidence interval (-155.75 to 69.75), we fail to reject the null hypothesis and conclude there is not sufficient evidence to warrant rejection of the claim that New Year's resolutions do not impact exercise time.
  5. Not enough information to calculate the confidence interval.

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