One of the bartleby experts helped me with this homework problem. I am having trouble figuring out where -1.64 came from on part (b). Look at the images below. 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?
One of the bartleby experts helped me with this homework problem. I am having trouble figuring out where -1.64 came from on part (b). Look at the images below.
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?
![Here
so reject
We conclude
time differs
accepted.
here,
- 206 =
cal 2 < -1.64
Ho at
that
P
a
d.o.s.
2.65 hours of quality
significantly from socially
3 hours figure.
100 (1) 1.
C. L
P[-2011 < 2 <^2x₁2] = 1.9
9292
X = 0.05
-1.96
1-α = 0.95
رطل
20DOM,
4
2
2
2412
evol
P[-1-96 < X-4 < 1.96] = 0195
0.
× - 6₂ × 1·.96 < 4 <
(110)4
2-1
7
0.025
spero t wolld
1:96
مل
x + 6 = 1196 ] = 0,
√√
j
[2.65.
·2·65- 1.5 * 1.96 < < 2.65 + 1.5
92
92
Pf 2.4 < 44 < 2.9] = 10.95
95%
c. t for
el
0.gs
[*196]
* 196
(2.4, 2.g) imple
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