The following 5 questions are based on this information. In a poll of 1000 Ameri
ID: 3216903 • Letter: T
Question
The following 5 questions are based on this information.
In a poll of 1000 American adults conducted on August 5-9, 2010, 44% (p¯=0.44) of respondents approve the job that President Barack Obama was doing handling the economy.
The goal is to construct a 90% confidence interval for the percentage (p) of American adults who approved of Barack Obama's handling of the economy around the period the poll was conducted. Please show all work
The standard error (SE) of p¯ is
Select one:
a. 0.016
b. 0.44
c. 0.0002
d. 0.0004
The critical value (CV) needed for 90% confidence interval estimation is
Select one:
a. 1.64
b. 1.96
c. 1.28
d. 2.58
The 90% confidence interval estimate of p is
Select one:
a. 0.44 ± 0.03
b. 0.44 ± 0.12
c. 0.44 ± 0.15
d. 0.44 ± 0.002
Suppose around the period the above poll was conducted, a political commentator made a personal statement saying that Obama's approval regarding handling of the economy is 50%.
In light of the sample evidence and at the 10% level of significance,
Select one:
a. We can reject the commentator's claim
b. We cannot reject the commentator's claim
Currently the sample size (n) is 1000. If we were to decease n to 500, the margin of error (ME) of the confidence interval estimate would
Select one:
a. increase
b. stays the same
c. decrease
d. be zero
Explanation / Answer
a) p = 0.44 , 1 -p = 0.56 , n = 1000
The standard error (SE) of p¯ is = sqrt(p *(1-p)/n)
= sqrt(0.44*0.56/1000)
= 0.016
b)
Critical value for 90% confidence interval
Step 1: Subtract the confidence level from 100% to find the level: 100% – 90% = 10%.
Step 2: Convert Step 1 to a decimal: 10% = 0.10.
Step 3: Divide Step 2 by 2 (this is called “/2”).
0.10 = 0.05. This is the area in each tail.
Step 4: Subtract Step 3 from 1 (because we want the area in the middle, not the area in the tail):
1 – 0.05 = .95.
Step 5: Look up the area from Step in the z-table. The area is at z=1.645. This is your critical value for a confidence level of 90%.
Critical value for 90% confidence interval = 1.64
c)
The 90% confidence interval estimate of p is
Confidence interval = p +/- critical value * SE
= 0.44 + /- 1.645 * 0.016
= 0.44 + / - 0.03