One of the bartleby experts helped me with this homework problem. I am having trouble reading the handwriting from parts (a) to (c). Can you rewrite the work that was provided for this homework problem? 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?
One of the bartleby experts helped me with this homework problem. I am having trouble reading the handwriting from parts (a) to (c). Can you rewrite the work that was provided for this homework problem?
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?
![2
(b) We
Ho:
fe
=
3 = 10
HI: μ = 2.65 < 3
2=
have
under Ho
√(x-1)
Let
to test
Then
L:
is
P= P(Z -2.7408]
= 0.00306
ワー
2,7408
Level of signific
be
0.05
Þ(= 0.00306) < d (= 0.05)
We Reject Hto
and conclude
/
that
2.65 hours of quality time
significantly from socially
accepted 3 hour figure
differs
cance
100 (1-0)% confidence interval (C#)
is
given as
Z Z
P[- 3042²
3042] =
1-2= 0.95, 2= 0,05, 2/2 = 0.095
3212= 30.025
= 1.96
Therefore,
3
P[-1.96 <√(-) <1-96] = 0.95
P[ 5-1.96.5 μ< = + 1.96 F ]
√n
P[ 2.65 0.25 μ< 2,65+ 0.25]
=P[ 2.4 < M < 2.9]
95% CI fort is
(2.4, २१).
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