Need help with parts (a) to (d) on this homework problem. Make sure the answers you provide are lengthy. Don't give short answers. Also, make sure your handwriting is neat and readable. Statistically speaking, the typical romantic couple spends 3 hours of quality time together each day, with a variance of 1.5 hours. During my teenage years, I was under the assumption that a friend and I were a couple, but she recently pushed back on that claim. So, I logged our time spent together over a period of 92 days. As it turned out, we spent 2.65 hours together on a typical day, again with a variance of 1.5 hours. Assuming that all of the time we spend together is “quality” and that relationship time spent is governed by the normal distribution, do I have sufficient statistical evidence to claim that we were, in fact, in a romantic relationship? (a) Find and interpret the z-score of our time spent together, specifically referencing what information the sign (positive/negative) of the z-score tells us. (b) Conduct a hypothesis test to determine whether our 2.65 hours of quality time differs significantly from the socially-accepted 3-hour figure. (c) Create and interpret a 95% confidence interval about our mean time spent together. (d) In light of all of this information, provide a conclusion: are we, or aren’t we?
Need help with parts (a) to (d) on this homework problem. Make sure the answers you provide are lengthy. Don't give short answers. Also, make sure your handwriting is neat and readable.
Statistically speaking, the typical romantic couple spends 3 hours of quality
time together each day, with a variance of 1.5 hours. During my teenage
years, I was under the assumption that a friend and I were a couple, but she
recently pushed back on that claim. So, I logged our time spent together over a
period of 92 days. As it turned out, we spent 2.65 hours together on a typical
day, again with a variance of 1.5 hours. Assuming that all of the time we spend
together is “quality” and that relationship time spent is governed by the normal
distribution, do I have sufficient statistical evidence to claim that we were, in
fact, in a romantic relationship?
(a) Find and interpret the z-score of our time spent together, specifically
referencing what information the sign (positive/negative) of the z-score
tells us.
(b) Conduct a hypothesis test to determine whether our 2.65 hours of quality
time differs significantly from the socially-accepted 3-hour figure.
(c) Create and interpret a 95% confidence interval about our mean time spent
together.
(d) In light of all of this information, provide a conclusion: are we, or aren’t
we?
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