Answer:
No, because the 95% confidence interval contains the hypothesized value of zero.
Step-by-step explanation:
Hello!
You have the information regarding two calcium supplements.
X₁: Calcium content of supplement 1
n₁= 12
X[bar]₁= 1000mg
S₁= 23 mg
X₂: Calcium content of supplement 2
n₂= 15
X[bar]₂= 1016mg
S₂= 24mg
It is known that X₁~N(μ₁; σ²₁), X₂~N(μ₂;δ²₂) and σ²₁=δ²₂=?
The claim is that both supplements have the same average calcium content:
H₀: μ₁ - μ₂ = 0
H₁: μ₁ - μ₂ ≠ 0
α: 0.05
The confidence level and significance level are to be complementary, so if 1 - α: 0.95 then α:0.05
since these are two independent samples from normal populations and the population variances are equal, you have to use a pooled variance t-test to construct the interval:
[(X[bar]₁-X[bar]₂) ±
*
]
![t_{n_1+n_2-2;1-/2}= t_{25;0.975}= 2.060](https://tex.z-dn.net/?f=t_%7Bn_1%2Bn_2-2%3B1-%2F2%7D%3D%20t_%7B25%3B0.975%7D%3D%202.060)
![Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} }= \sqrt{\frac{11*529+14*576}{12+15-2} } = 23.57](https://tex.z-dn.net/?f=Sa%3D%20%5Csqrt%7B%5Cfrac%7B%28n_1-1%29S%5E2_1%2B%28n_2-1%29S%5E2_2%7D%7Bn_1%2Bn_2-2%7D%20%7D%3D%20%5Csqrt%7B%5Cfrac%7B11%2A529%2B14%2A576%7D%7B12%2B15-2%7D%20%7D%20%3D%2023.57)
[(1000-1016)±2.060*23.57*
]
[-34.80;2.80] mg
The 95% CI contains the value under the null hypothesis: "zero", so the decision is to not reject the null hypothesis. Then using a 5% significance level you can conclude that there is no difference between the average calcium content of supplements 1 and 2.
I hope it helps!
Answer:
8
Step-by-step explanation:
4 is the base. 8 are the sides
Answer:
Step-by-step explanation:
The compound amount formula is A = P(1 + r/n)^(n*t), where n is the number of times interest is compounded per year and t is the number of years.
We could let n = 365 (since there are 365 days in each year). Then,
A = P(1 + r/365)^(365*t).
Then, in this case, A = $10,000(1 + 0.052/365)^(365*20), or
A = $10,000(1 + 0.000142)^7300, or
A = $10,000(2.829)
A = $28,290.07
Answer:
C. $30
Step-by-step explanation:
Given
Cost = $240
down payment = $60
remainder = $240 - $60 = $180
given that the remainder is to be split into 6 equal paments
each payment = $180 ÷ 6 = $30