Question

The end-of-year report for last year indicated the average sell price for houses in Las Cruces is $190,000. A realtor wants to conduct an experiment to show that the house sell price has increased this year compared to last year. He randomly selected 35 houses that are sold this year, and the data is provided in the Excel file provided.

1. Make a boxplot on the house sell price, and identify if there are outliers observed from the data. Attach the boxplot here.
2. Take out the outliers (simply delete the outlier data). There is no other information provided for the study, which hypothesis test will be appropriate to address the research question? (z test or t test)
3. Use Excel to conduct the hypothesis test. Attach the Excel output here, then write the 5-step procedure of the test below. (Don’t forget to create the dummy variable before choosing the “t test: Two-Sample Assuming Unequal Variances”)

4. Based on your conclusion of part (3), what type of error could you possibly make? (type I or Type II)

A 5 6 1 House Sell Price 2 187000 3 181000 4 184000 188000 196000 7 198000 8 500000 9 187000 10 188000 11 189000 12 201000 13 202000 14 202000 15 173000 16 194000 17 188000 18 199000 19 195000 20 183000 21 185000 22 180000 23 187000 24 213000 25 207000 26 207000 27 200000 28 200000 29 218000 30 189000 31 197000 32 208000 33 188000 34 212000 35 195000 36 185000 37

Answer 1

Given that,
population mean(u)=190000
sample mean, x =203028.571
standard deviation, s =51937.592
number (n)=35
null, Ho: μ=190000
alternate, H1: μ>190000
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.691
since our test is right-tailed
reject Ho, if to > 1.691
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =203028.571-190000/(51937.592/sqrt(35))
to =1.484
| to | =1.484
critical value
the value of |t α| with n-1 = 34 d.f is 1.691
we got |to| =1.484 & | t α | =1.691
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :right tail - Ha : ( p > 1.4841 ) = 0.0735
hence value of p0.05 < 0.0735,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=190000
alternate, H1: μ>190000
test statistic: 1.484
critical value: 1.691
decision: do not reject Ho
p-value: 0.0735
we do not have enough evidence to support the claim that an experiment to show that the house sell price has increased this year compared to last year.
Type 2 error is possible because it fails to reject the null hypothesis