sgalvis455
16.06.2020 •
Mathematics
Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advices and support from the accountant if the client were audited. A large accounting firm is trying to determine what fee to charge for nextyear's returns. In previous years, the actual mean cost to the firm for attending a client audit session was $690. To determine if this cost has changed, the firm randomly samples 35 client audit fees. The sample mean audit cost was $700 with a standard deviation of $65.
Required:
a. Develop a 90% confidence interval estimate for the mean audit cost.
b. Based on your confidence interval, what do you think of the claim that the mean cost has changed?
1. The interval does not contain the historical data mean $690, which supports claim the mean cost has changed.
2. The interval contains historical data mean $690, which supports the claim the mean cost has changed.
3. The interval does not contains historical data mean $690, which does not support the claim it has changed.
4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.
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Ответ:
a) $700+/-$18.07
Therefore,the 90% confidence interval (a,b)
= ($681.93, $718.07)
b) 4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $700
Standard deviation r = $65
Number of samples n = 35
Confidence interval = 90%
z(at 90% confidence) = 1.645
a. Develop a 90% confidence interval estimate for the mean audit cost.
Substituting the values we have;
$700+/-1.645($65/√35)
$700+/-1.645($10.98700531147)
$700+/-$18.07362373736
$700+/-$18.07
Therefore,the 90% confidence interval (a,b) = ($681.93, $718.07)
b) Since, $690 is contained between the 90% confidence interval of ($681.93, $718.07). It implies that the mean cost has not changed.
4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.
Ответ: