Question 1160306
With appropriate assumptions including random sampling,
Ho: price is < =92
Ha: it is >92
alpha=0.05 p{reject Ho|Ho true|
test statistic is a z(0.95, df=99) The sd is given for the population
critical value z>1.645
z=(92.80-92)/8.5/sqrt(100)
=0.94
fail to reject Ho; insufficient evidence to say the mean price is >92 birr

The y-intercept is the weight of a person who doesn't consume any calories. That makes no sense, but intercepts in many regression lines are far from the data points and may make no sense. 

The slope of the line is weight per calories eaten, and suggests that weight increases 1 pound per every 200 cal in the diet eaten (200*0.005=1). This suggests that as people consume more and more calories on a daily basis their weight rises.  That in itself is qualitatively true, but the number of calories we consume on a daily basis is from 0 (sick or fasting) to maybe a few thousand unless somebody has a job or exercise leading to consuming of many thousands of calories. In other words, the effective domain is limited.

The half-interval is 4 = z*sigma/sqrt(n)
4 sqrt(n)=z*sigma=1.96*215
sqrt(n)=1.96*215/4=105.35
n=11,099 rounding up

SEM=z*sigma/sqrt(n)=20. z is not given, so will assume it is 1.96
1.96*500/sqrt(n)=20
1.96*500/20=sqrt(n)=49
n=2401

The SEM is 20, the point estimate will be within 25 meaning it will be with 1.25 sd of the mean with 0.7887 probability.