Question

The following is a stem and leaf chart of the head circumferences (in centimeters) of two-month old female babies:

Stem (1=1cm)	Leaf (1=0.1cm)		Stem (1=1cm)	Leaf (1=0.1cm)
34	4		39	23566699
35			40	00112222333355677889
36	39		41	0000236
37	8		42	006
38	123669		43	67

Is there enough evidence to indicate that the typical two-month old female baby has a head circumference larger than 39.0cm, with a 0.05 significance level? Justify your answer. Use s = 1.6395 cm.

Answer 1

To perform the hypothesis test, the data values are retrieved from the stem and leaf plot in excel. The screenshot is shown below,

Since we are comparing one sample mean with the population mean and the population standard deviation is not known, the t-test for One Population Mean is be used to test the following hypothesis,

Hypothesis

The Null and Alternative Hypotheses are defined as,

This is a right-tailed test.

The significance level = 0.05

Test-statistic

The t statistic is obtained using the formula,

For calculation purpose, the mean and standard deviation are obtained in excel using the function =Average() and =STDEV(). The screenshot is shown below,

Now,

P-value

The p-value is obtained from the t distribution table for t = 4.3130 and degree of freedom = n - 1 = 50 - 1 = 50. (In excel use function =T.DIST.RT(4.3130,49))

Conclusion

Since the P-value is less than 0.05 at a 5% significance level, the null hypothesis is rejected. Hence there is sufficient evidence to conclude that the typical two-month-old female baby has a head circumference larger than 39.0cm.