Q.97 Suppose that an accounting firm ... [FREE SOLUTION]

魅影直播

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 魅影直播 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 8: Q.97 (page 484)

Suppose that an accounting firm does a study to determine the time needed to complete one person鈥檚 tax forms. It
randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The
population distribution is assumed to be normal.
a. I. $X$ =
ii. 蟽 =
iii. n =
b. In words, define the random variables X and $X$
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a 90% confidence interval for the population mean time to complete the tax forms.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey,
what changes should it make?
f. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to
the level of confidence? Why?
g. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to
within one hour. How would the number of people the firm surveys change? Why?

Short Answer

Expert verified

a. I. $x$ =23.6hours

ii. $蟽$ =7

iii. n= 100

b.Time completed to form the separate tax form is X and the mean time to complete tax forms from a sample of 100 customers is X

c. Normal distribution use for the problem. As we know that sample size is more than 30 for the standard deviation of the population.

d. i. CI= (22.228, 24.972)

ii.

iii. EBM = 1.151

e. It is likely that the sample size will need to be adjusted.

f. Because of same size error bound

g. According to the error bound formula, 206 people in the firm.

Step by step solution

Solution of A

I The sample mean time to complete 100 tax forms is 23.6 hours

$x$ $= 23.6 h o u r s$

ii. Standard deviation of time to complete the tax forms is 7 hours,

$伪 = 7$

iii. Number of people who were surveyed for the time to complex tax forms is,

$n = 100$

Solution of B

Time completed to form the separate tax form is X and the mean time to complete tax forms from a sample of 100 customers is X

Solution of C

Normal distribution use for the problem. As we know that sample size is more than 30 for the standard deviation of the population n and the distribution is N $(\begin{matrix} 23.6, 7.0 \\ \sqrt{100} \end{matrix})$ .

Solution of D

I. State the range of confidence.

CI stands for "Common Interest"

CI= (22.228, 24.972)

ii. The graph is given below,

iii. The error bound is calculated from the formula,

EBM = $\frac{U p p e r l i m i t - I o w e r l i m i t}{2}$

EBM = $\frac{24.751 - 22.440}{2}$

$E B M = 1.151$

Solution of E

It is likely that the sample size will need to be adjusted. The firm requires the confidence level to be determined, after which we must use the error bound formula to calculate the required sample size.

Solution of F

Because of the same size error constraint, the confidence level would decrease for the same size interval and likewise for a smaller sample size.

Solution of G

According to the error bound formula, 206 people in the firm needs to be surveyed as the confidence level rises, requiring an increase in the sample size or the error bound.