Download 16) Use graphs to compare the head circumference of two months

HEAD CIRCUMFERENCE
Chapter 8 – Confidence Intervals about a Population Mean mu
6) a) Estimate the mean head circumference of all baby-girls that are two months old by
constructing a 99% confidence interval.

We start by selecting a simple random sample of size n. In our calculator we actually
have one such a sample labeled FHED

We calculate the mean of the selected sample. This is our point estimate.
x = 40.048
Our point estimate is
(Do STAT, CALC, 1-Var Stats on FHED to get the statistics)

To fine-tune our estimate, we find a confidence interval which is a range (or interval)
of values that is likely to contain the true value of the population mean.
Show all work, and then check with a calculator feature (Are you using z or t?
Why?)
We are using t because we are not given the standard deviation of the population
σ; we have the standard deviation of the sample which is 1.639
(Our sample statistics are: x = 40.048, s = 1.639, n = 50)
The degrees of freedom are 49. Since we don’t have that value in our table we’ll use 49.
The t-score for a 99% confidence interval is 2.69 (see t-table on the back cover of book)
s
s
   xt*
n
n
1.639
1.639
40.048  2.69 *
   40.048  2.69 *
50
50
40.048  .62351    40.048  .62351
xt*
39.42    40.67
For calculator feature use STAT, arrow to TESTS, and select 8:TInterval,
select DATA option enter the required information, and CALCULATE
b) Complete the following:
(i) With 99% confidence we can say that the mean head circumference of two-month-old
baby girls is __40.048 cm____ with a margin of error of __.624 cm_____
(ii) We are _99___% confident that the interval from ___39.42_ to ___40.67___ actually does
contain the true value of the population mean μ. This means that if we were to select many
different samples of the same size and construct the corresponding confidence intervals, in the
long run __99____% of them would actually contain the value of μ.
(iii) For 99% of such intervals, the sample mean would not differ from the actual population
mean by more than __.624 cm_____
Page 6
HEAD CIRCUMFERENCE
Chapter 8 – Confidence Intervals about a Population Mean mu
7) a) Estimate the mean head circumference of all baby-boys that are two months old by
constructing a 99% confidence interval.

We start by selecting a simple random sample of size n. In our calculator we actually
have one such a sample labeled MHED

We calculate the mean of the selected sample. This is our point estimate.
x = 41.098
Our point estimate is
(Do STAT, CALC, 1-Var Stats on MHED to get the statistics)

To fine-tune our estimate, we find a confidence interval which is a range (or interval)
of values that is likely to contain the true value of the population mean.
Show all work, and then check with a calculator feature. (Are you using z or t?
Why?)
We are using t because we are not given the standard deviation of the population
σ; we have the standard deviation of the sample which is 1.498
(Our sample statistics are: x = 41.098, s = 1.498, n = 50)
The degrees of freedom are 49. Since we don’t have that value in our table we’ll use 49.
The t-score for a 99% confidence interval is 2.69 (see t-table on the back cover of book)
s
s
   xt*
n
n
1.498
1.498
41.098  2.69 *
   41.098  2.69 *
50
50
41.098  .56987    41.098  .56987
xt*
40.53    41.67
For calculator feature use STAT, arrow to TESTS, and select 8:TInterval,
select DATA option enter the required information, and CALCULATE
b) Complete the following:
(i) With 99% confidence we can say that the mean head circumference of two-month-old
baby boys is _41.098 cm_ with a margin of error of __.57 cm____
(ii) We are _99___% confident that the interval from ___40.53 to ____41.67__ actually does
contain the true value of the population mean μ. This means that if we were to select many
different samples of the same size and construct the corresponding confidence intervals, in the
long run ___99___% of them would actually contain the value of μ.
(iii) For 99% of such intervals, the sample mean would not differ from the actual population
mean by more than ___.57 cm____
2
c) Compare with the results of the previous page. Does there appear to be a significant
difference between the two genders? Explain.
For girls the interval is (39.42, 40.67)
These are possible values for the head circumference of ALL two-month-old baby girls
For the boys the interval is (40.53, 41.67)
These are possible values for the head circumference of ALL two-month-old baby boys
Since the intervals overlap, it may be that the head circumference of two-month-old
baby boys and girls is the same.
3