Answer:
Step-by-step explanation:
A signed number means that the number uses a plus or minus sign in front of it.
A
Her account will get 200 dollars larger so you will use + 200
B
The temperature is 12 degrees below zero (cold!!!) so you will write - 12
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) ± * ]
[(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:
tan∅ = 3√29/10
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
cos∅ = adjacent/hypotenuse
Since we are given cos∅ = 10/19, we know that one leg is 10 and the hypotenuse is 19. We need to find the missing leg length:
10² + b² = 19²
b² = 19² - 10²
b = √261
b = 3√29
We know that tan∅ equals opposite over adjacent. Our adjacent is given to us by cos∅, so we simply plug in our values:
tan∅ = opposite/adjacent
tan∅ = 3√29/10
Let x = minimum electric rate (Cents/kWh)
Total months in 12 years is 12*12 = 144 m
1st freezer
Total cost over 12 years is
623.95 (cost) + (90 kWh/m)*(144 m)(x/100 $/kWh)
= 623.95 + 129.6x
2nd freezer
Total cost over 12 years is
500 + 100*144*(x/100)
= 500 + 144x
For the 1st freezer to cost less over 12 years,
623.95 + 129.6x < 500 + 144x
123.95 < 14.4x
8.61 < x
Answer: The minimum rate is 8.61 cents per kWh