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You are concerned that you consume too much caffeine. However, you love pumpkin spice lattes. You...

You are concerned that you consume too much caffeine. However, you love pumpkin spice lattes. You decide to measure the amount of caffeine in your 12 oz. pumpkin spice late over 5 days (assume you only drink one a day). You find that the sample mean of caffeine from these 5 lattes is 72.8 mg with a sample standard deviation of 11.2 mg.

  • (a) Calculate a 95% confidence interval for the mean amount of caffeine in pumpkin spice lattes of this size.
  • (b) Assume that you want to keep your caffeine consumption under 80 mg per day. Is there evidence that the mean amount of caffeine in these pumpkin spice lattes is less than 80? (Use a one-sided test and report level of significance).
  • (c) Now, if you wanted to keep your caffeine consumption under 95 mg per day, is there evidence that the mean amount of caffeine in these lattes is less than 95? (Use a one-sided test and report level of significance).
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