Answer:
Step-by-step explanation:
Hello!
To test if calcium reduces the symptoms of PMS two independent groups of individuals are compared, the first group, control, is treated with the placebo, and the second group is treated with calcium.
The parameter to be estimated is the difference between the mean symptom scores of the placebo and calcium groups, symbolically: μ₁ - μ₂
There is no information about the distribution of both populations X₁~? and X₂~? but since both samples are big enough, n₁= 228 and n₂= 212, you can apply the central limit theorem and approximate the sampling distribution to normal X[bar]₁≈N(μ₁;δ₁²/n) and X[bar]₂≈N(μ₂;δ₂²/n)
The formula for the CI is:
[(X[bar]₁-X[bar]₂) ± 
* 
]
95% confidence level 
(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53
X₁: Mood swings score of a participant of the placebo group.
X₂: Mood swings score of a participant of the calcium group.
[(0.70-0.50) ± 1.96 * 
]
[0.076; 0.324]
(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40
X₁: Crying spells score of a participant of the placebo group.
X₂: Crying spells score of a participant of the calcium group.
[(0.39-0.21) ± 1.96 * 
]
[0.088; 0.272]
(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45
X₁: Aches and pains score of a participant of the placebo group.
X₂: Aches and pains score of a participant of the calcium group.
[(0.45-0.37) ± 1.96 * 
]
[-0.019; 0.179]
(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61
X₁: Craving for sweets or salts score of a participant of the placebo group.
X₂: Craving for sweets or salts score of a participant of the calcium group.
[(0.60-0.44) ± 1.96 * 
]
[0.032; 0.287]
I hope this helps!
