Question

6.38 Reporting margins of error. A U.S. News &
World Report article of July 17, 2014, reported Commerce Department estimates of changes in the
construction industry:

Construction fell 9.3 percent last month to a
seasonally adjusted annual rate of 893,000 homes,
the Commerce Department said Thursday.
If we turn to the original Commerce Department report (released on July 17, 2014), we read:

Privately-owned housing starts in June were at a
seasonally adjusted annual rate of 893,000. This
is 9.3 percent (10.3%) below the revised May
estimate of 985,000.

(a) The 10.3% figure is the margin of error based on a
90% level of confidence. Given that fact, what is the 90%
confidence interval for the percent change in housing
starts from May to June?

(b) Explain why a credible media report should state:
“The Commerce Department has no evidence that
privately-owned housing starts rose or fell in June from
the previous month.”

Answer 1

Solution-A

90% confidence interval for p is

sample proportion-margin of error,sample proportion+margin of error

9.3-10.3,9.3+10.3

-1.3,19.6

90% lower limit for p=-1.3%

90% upper limit for p=19.6%

Solution-b:

Ho:p=9.3

Ha:p not = 9.3

Since the 90% confidence interval for p

90% lower limit for p=-1.3%

90% upper limit for p=19.6%

contains 9.3

Accept null hypothesis and conclude that

there is no sufficient evidence at 90% confidence interval to conclude that

he Commerce Department has no evidence that
privately-owned housing starts rose or fell in June from
the previous month.”