Which of the following statements are not true in developing a confidence interval for the population mean?
1 answer:
Answer:
b) The width of the confidence interval becomes narrower when the sample mean increases.
Step-by-step explanation:
The confidence interval can be calculated as:
a) The width of the confidence interval becomes wider as the confidence level increases.
The above statement is true as the confidence level increases the width increases as the absolute value of test statistic increases.
b) The width of the confidence interval becomes narrower when the sample mean increases.
The above statement is false. As the sample mean increases the width of the confidence interval increases.
c) The width of the confidence interval becomes narrower when the sample size n increases.
The above statement is true as the sample size increases the standard error decreases and the confidence interval become narrower.
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Answer:
Part a: From column 1 of the attached Wage and Tax statement, the gross pay is $34854.
Part b: From column 17 of the attached Wage and Tax statement, she paid $1762.39 in state income tax.
Part c: It should be $2160.95 instead of $2164.44
Part d: It should be $505.38 instead of $467.68
Part e: FICA Tax is $2665.38
Part f: She owes the difference $16.52 to the Federal Tax.
Step-by-step explanation:
As data was missing from the question, the complete question is found online and is attached herewith.
Part a:
From column 1 of the attached Wage and Tax statement, the gross pay is $34854.
Part b:
From column 17 of the attached Wage and Tax statement, she paid $1762.39 in state income tax.
Part c:
For 2012, Social Security Tax is given as 6.2% of the gross pay so
Item 4 should then be
6.2% x Gross Income
6.2% x 34854
.062 * 34854 = 2160.95
It should be $2160.95 instead of $2164.44
Part d
For 2012, Medicare Tax is given as 1.45% of the gross pay so
Item 6 should then be
1.45% x Gross Income
1.45% x 34854
.0145 * 34854 = 505.38
It should be $505.38 instead of $467.68
Part e
FICA tax is given as sum of Social security tax and Medicare taxes. This is given as
FICA Tax=Social Security Tax+Medicare Tax
FICA Tax=$2160+$505.38
FICA Tax=$2665.38
FICA Tax is $2665.38
Part f
From the attached table, with $32104 as the taxable income, as the head of household she owes $4199 in Federal tax.
From the attached wages and tax statement in column 2, she paid $4182.48. Thus she owes the difference $16.52 to the Federal Tax.
