Question

the human relations department of electronics incorporated would like to include a dental plan as part of the benefits package. the question is: how much does a typical employee and his or her family spend per year on dental expenses? a sample of 45 employees reveals the mean amount spent last year was $1,820, with a standard deviation of $660.a. compute a 95% confidence interval to estimate the population mean dental expense. (round your answers to the nearest whole dollar amount.)b. the information from part (a) was given to the president of electronics incorporated. he indicated he could afford $1,700 of dental expenses per employee. is it possible that the population mean could be $1,700? justify your answer.multiple choiceyesnovery unlikely

Answer 1

A 95% confidence interval for the population mean dental expense was computed, resulting in a range of $1,628 to $2,012. Considering this interval, it is possible for the population mean to be $1,700 as it lies within the computed range.

Step-by-step explanation:

To compute a 95% confidence interval for the population mean dental expense, we use the formula for a confidence interval when the population standard deviation is known and the sample size is large (n > 30), but since the population standard deviation is not specified, we'll assume the sample standard deviation is a good approximation. The formula is:

CI = X± (z* * (σ/√n))

Where X is the sample mean, z* is the z-score for the desired confidence level, σ is the standard deviation of the sample, and n is the sample size.

Given that X = $1,820, σ = $660, n = 45, and the z-score for a 95% confidence interval is approximately 1.96:

CI = $1,820 ± (1.96 * ($660/√45))

CI = $1,820 ± $192

CI = ($1,628, $2,012)

For part b): Looking at the confidence interval computed, it includes $1,700 within its range which indicates that it's possible for the population mean to be $1,700, making it within the realm of possibility.

Answer 2

The 95% confidence interval for the population mean dental expense ranges from $1,628 to $2,013. It is possible that the population mean could be $1,700 since it lies within the calculated confidence interval.

Step-by-step explanation:

To compute a 95% confidence interval for the population mean dental expense, we use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / sqrt(Sample Size))

Given the sample mean is $1,820, standard deviation of $660, and sample size is 45, first we need to find the critical value for a 95% confidence level. Since the sample size is large (n > 30), we can use the z-distribution, where the z-value for a 95% confidence interval is approximately 1.96.

Confidence Interval = $1,820 ± (1.96) * ($660 / sqrt(45))

Calculating the margin of error:

Margin of Error = 1.96 * ($660 / sqrt(45)) ≈ $192.60

Therefore, the 95% confidence interval is $1,820 ± $192.60, or ($1,628 to $2,013).

Regarding part b, it is possible that the population mean could be $1,700, as $1,700 is within the lower bound of the confidence interval calculated in part a.