Chapter 10: Q. 10.49 (page 416)

Nigerian Spleen Length. O.Ehimwenma and M.Tagho, researchers in Nigeria, were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in te world. They published their findings in the article "Determination of Normal Dimensions of the Spleen by Ultrasound in an Endemic Tropical Environment" (Nige4ian Medical Journal, Vol. $52$ , No. $3$ ,pp. $198 - 203$ ). The researchers randomly samples $91$ males and $109$ females in Nigeria. The mean and standard deviation of the spleen lengths for the males were $11.1$ cm and $0.9$ cm respectively, and those for the females were $10.1$ cm and $0.7$ cm, respectively. At the $1 %$ significance level, do the data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians?

Short Answer

Expert verified

The data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians at $1 %$ significance level.

Step by step solution

Step 1. Given information

Significance level $= 1 %$ .

Step 2. Definition for Null and Alternative hypothesis:

Null Hypothesis:

$H_{0} : μ_{1} = μ_{2}$

That is, the data does not provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians.

Alternative Hypothesis:

$H_{0} : μ_{1} \neq μ_{2}$

That is, the data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians.

Step 3. The Given significance level is, α=0.01.

Now compute the value of the test statistic by using MINITAB.

MINITAB Procedure:

Choose Stat > Basic Statistics > $2$ -Sample $t$ .
Choose Summarized data.
In first, enter Sample size as $91$ , Mean as $11.1$ , Standard deviation as $0.9$ .
In second, enter Sample size as $109$ , Mean as $10.1$ , Standard deviation as $0.7$ .
Select Assume equal variances.
Choose options.
In confidence level enter $99$ .
In Alternative select not equal.
Click OK in all the dialogue boxes.

Step 4. MINITAB output:

Two-Sample T-Test and CI

From the MINITAB output, the value of test statistic is $8.83$ .

Step 5. Find the P-value:

From the MINITAB output, the $P$ -value is, $0.0000$ .

If $P \leq α$ , then reject the null hypothesis. Here, the $P$ -value is $0.000$ which is less than the level of significance. That is, $P (= 0.000) < α (= 0.01)$ .

Therefore, the null hypothesis is rejected at $1 %$ level. Thus, it can be conclude that the test results are statistically significant at $1 %$ significance level.