Question

Frigerio et al. (1991) measured the energy consumed in 26 Gambian women. Thirteen of the individuals studied were women who were breastfeeding (L) and the rest were non-pregnant women who were not breastfeeding (NENL). The following data was reported:

Muestra Consumo de energía (kJ/d) 5289, 6209, 6054. 6665, 6343. 7699, 5678. 6954. 6916. 4770, 5979, 6305, 6502 NENL 9920, 8581, 9305, 10765, 8079, 9046, 7134, 8736, 10230,7121 8665, 5167, 8527

Do these data provide enough evidence to conclude that the populations sampled differ with respect to the average energy consumption? Note: the probability of not rejecting true H₀ equal to 0.99, the probability of rejecting false H₀ equal to 0.9 and the population variances equal to 569986.4 and 2181940 respectively.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁$\neq$ u ₂

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 460.094
DF = 24
t = [ (x₁ - x₂) - d ] / SE

t = -5.00

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 24 degrees of freedom is more extreme than -5.00; that is, less than -5.00 or greater than 5.00.

Thus, the P-value = less than 0.001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the populations sampled differ with respect to the average energy consumption.