Question

1.In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a sample standard deviation of $3,156.

Assume the underlying distribution is approximately normal.

Which distribution should you use for for determining a confidence interval for estimating the population mean for used car sales costs?

What is the number of degrees of freedom (df) for this problem.

Answer this question by:

Select the correct distribution and enter the appropriate letter.

Enter the degrees of freedom (df) for this problem. If this is an inappropriate question for the distribution being used enter the number 0

a   Normal Distribution

b     t Distribution

c     Uniform

d     Chi Sq distribution

Enter the answers for the 2 questions being asked in the same order in which they were asked.

________________

Define the random variable X by selecting the appropriate letter below.

a     An individual data item randomly selected from the population, some times referred to as the parent population.

b     The average of n individual data item randomly selected from the parent population. In this question n is 84.

Define the random variable X ¯ (Xbar) by selecting the appropriate letter below.

c     An individual data item randomly selected from the population, sometimes referred to as the parent population.

d     The average of n individual data item randomly selected from the parent population. In this question n is 84.

Enter your answers in the order in which the questions were asked.

________________

Construct a 95% confidence interval for the population mean time wasted.

Enter your answers rounded to 0 decimal places (Enter answer as an integer).

In the two answer locations provided enter the lower bound of the confidence interval first followed by the upper bound.

________________

What is meant by the term “95% confident” when constructing a confidence interval for a mean?

a.    If we took repeated samples, approximately 95% of the samples would produce the same confidence interval.

b     If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the sample mean.

c     If we took repeated samples, the sample mean would equal the population mean in approximately 95% of the samples

d     If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean..

Enter the correct answer by selecting the appropriate letter

2.

The owner of the Britten's Egg Farm wants to estimate the mean number of eggs produced per chicken.  A representative random sample of 25 chickens show they produce an average of 20 eggs per month with a sample standard deviation (s) of 2 eggs per month. The distribution is known to be symmetrical and is close enough to normal to be treated as a normal distribution.

Answer the following questions related to the above paragraph and calculate a 90% confidence interval for the mean number of eggs produced per chicken on the Britten's Egg Farm.

a     What is the point estimate of the mean number of eggs produced per chicken?
       Enter answer with 0 decimal places (integer).

______

b     What is the appropriate distribution for calculating a 90% confidence interval?

a     Uniform distribution

b     Normal distribution

c     t distribution

d     Chi Square distribution

Answer this question by entering the appropriate letter.

______

c     The degrees of freedom (df) for this problem is?
       Enter Na or 0 for the df if the appropriate distribution does not required a df.

______

e     The 90% conference interval for the mean number eggs produced per month is:

Enter the lower and upper limits for the conference interval by entering the lower limit first.
Rounded each conference limit to 1 decimal point.

____________

  

F     Prior to this study the owner of the Britten's Egg Farm Egg Farm believed the mean amount off eggs produced per month on his farm was 22.

Does the study support his belief with a 90% confidence?

a     Yes. The mean amount of eggs produced per month on his farm could be 22 per month because the number 22 is not contained in the confidence interval.

b     Yes. The mean amount of eggs produced per month on his farm could be 22 per month because the number 22 is contained in the confidence interval.

c     No. The mean amount of eggs produced per month on his farm is most likely not 22 per month because the number 22 is not contained in the confidence interval.

d     No. The mean amount of eggs produced per month on his farm is most likely not 22 per month because the number 22 is contained in the confidence interval.

e    The owner can not comment on the mean amount of eggs produced per month on his farm because the confidence interval is based upon a sample.

Enter the correct answer by selecting and entering the appropriate letter.

_____

Answer 1

Which distribution should you use for for determining a confidence interval for estimating the population mean for used car sales costs?

here n=84 large sample follows normal distribution according to central limit theorem.
here use t distribution ,since sample standard deviation is given

t Distribution

Enter the degrees of freedom (df) for this problem. If this is an inappropriate question for the distribution being used

df=n-1=84-1=83

df=83

Define the random variable X by selecting the appropriate letter below.

Here we are estimating the population mean for used car sales costs by confidence interval.

a     An individual data item randomly selected from the population, some times referred to as the parent population.

Define the random variable X ¯ (Xbar) by selecting the appropriate letter below.

d     The average of n individual data item randomly selected from the parent population. In this question n is 84.

Construct a 95% confidence interval for the population mean time wasted

xbar-tc*s/sqrt(n),xbar+tc*s/sqrt(n)

alpha=0.05

alpha/2=0.05/2=0.025

=T.INV(0.025,83)

=1.98895978

so 95 % confidence interval for mean

6425-1.98895978*3156/sqrt(84),6425+1.98895978*3156/sqrt(84)

5740.106, 7109.894

5740,7110

(rounding to zero decimals)

5740<mu<7110

5740,7110

What is meant by the term “95% confident” when constructing a confidence interval for a mean?

d     If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean..

ANSWERS:

t Distribution

a     An individual data item randomly selected from the population, some times referred to as the parent population.

d     The average of n individual data item randomly selected from the parent population. In this question n is 84.

5740,7110

d     If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean..