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Harrisburg University of Science and Technology **We aren't endorsed by this school

Course

ANLY 502-51- A

Subject

Statistics

Date

Aug 16, 2023

Pages

3

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# On your own
# So far, we have only focused on estimating the mean living area in homes in Ames.
# Now you'll try to estimate the mean home price.
# .Take a random sample of size 50 from
price . Using this sample, what is your
#
best point estimate of the population mean?
> set.seed(520)
> sampprice1 = sample(price, 50)
> summary(sampprice1)
Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
82000
130250
157000
177205
216250
421250
#Answer: point estimate of the population mean was 177205.
# .Since you have access to the population, simulate the sampling distribution
# for $\bar{x}_{price}$ price (sampling mean of price ) by taking 5000 samples from
# the population of size 50 and computing 5000 sample means.
# Store these means in a vector called
sample_means50 . Plot the data,
# then describe the shape of this sampling distribution.
# Based on this sampling distribution, what would you guess the mean home price of
# the population to be? Finally, calculate and report the population mean.
> set.seed(520)
> sample_means50 <- rep(NA, 5000)
> for(i in 1:5000){
+
samp <- sample(price, 50)
+
sample_means50[i] <- mean(samp)
+ }
> hist(sample_means50, breaks = 25)
> summary(sample_means50)
Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
144726
172613
180309
180823
188420
229463
> summary(price)
Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
12789
129500
160000
180796
213500
755000
>

#Answer:
#The sampling distribution is close to a normal distribution.
#I would guess the mean home price of the population to be 180823.
#The population mean was 180796.
# .Change your sample size from 50 to 150, then compute the sampling distribution
# using the same method as above, and store these means in a new vector called
# sample_means150 . Describe the shape of this sampling distribution, and compare
# it to the sampling distribution for a sample size of 50.
# Based on this sampling distribution, what would you guess to be the mean sale
# price of homes in Ames?
> set.seed(520)
> sample_means150 <- rep(NA, 5000)
> for(i in 1:5000){
+
samp <- sample(price, 150)
+
sample_means150[i] <- mean(samp)
+ }
> hist(sample_means150, breaks = 25)
> summary(sample_means150)

Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
160189
176417
180707
180865
185204
203445
#Answer:
#The sampling distribution is close to a normal distribution.
#Compared to the previous distribution, this distribution has a smaller spread.
#I would guess the mean home price of the population to be 180865.
# .Of the sampling distributions from 2 and 3, which has a smaller spread?
# If we're concerned with making estimates that are more often close to the
# true value, would we prefer a distribution with a large or small spread?
#Answer:
#Sampling distribution from 3 has a smaller spread.
#I would prefer a distribution with a small spread.

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