Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean weight loss yield of the powder diet and μ2 be the mean weight loss yield of the liquid diet.
The random variable is μ1 - μ2 = difference in the mean weight loss yield of the powder diet and the mean weight loss yield of the liquid diet.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
This us a left tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(μ1 - μ2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 42
μ2 = 45
s1 = 12
s2 = 14
n1 = 49
n2 = 36
t = (42 - 45)/√(12²/49 + 14²/36)
t = - 1.04
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [12²/49 + 14²/36]²/[(1/49 - 1)(12²/49)² + (1/36 - 1)(14²/36)²] = 70.28/1.03
df = 68
We would determine the probability value from the t test calculator. It becomes
p value = 0.15
Assuming a significance level of 0.05, then
Since alpha, 0.05 < than the p value, 0.15, then we would fail to reject the null hypothesis. Therefore, we can conclude that at a 5% significance level, the liquid diet does not yield a higher mean weight loss than the powder diet.
