A contemporary building has a window in the shape of a parallelogram with a base of 90 in and an adjacent side of 40 in. How man
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Answer:
a) Null hypothesis : H₀ : μ = 5.5
Alternative Hypothesis : H₁ : μ < 5.5
b) The test statistic
|t| = |-3.33| = 3.33
c) P - value lies between in these intervals
0.001 < P < 0.005
Step-by-step explanation:
<u><em>Step( i )</em></u>:-
Given data the Population mean 'μ' = 5.5
The small sample size 'n' = 16
The sample mean (x⁻) = 5.25
Given the percentage of SiO2 in a sample is normally distributed with a sigma of 0.3.
<u><em> Null hypothesis : H₀ : μ = 5.5</em></u>
<u><em> Alternative Hypothesis : H₁ : μ < 5.5</em></u>
Level of significance ∝ = 0.01
<u><em>Step(ii)</em></u>:-
The test statistic
On calculation , we get
t = -3.33
|t| = |-3.33| = 3.33
<u><em>Step(iii)</em></u>:-
<u><em>P - value</em></u>
<u><em>The degrees of freedom γ = n-1 = 16-1 =15</em></u>
The calculated value t = 3.33 (check t-table) lies between the 0.001 to 0.005
0.001 < P < 0.005
<u>Condition(i)</u>
P - value < ∝ then reject H₀
<u>Condition(ii)</u>
P - value > ∝ then Accept H₀
we observe that 0.001 < P < 0.005
P- value < 0.01
we rejected H₀
<em>(or)</em>
The tabulated value = 2.60 at 0.01 level of significance with '15' degrees of freedom
The calculated value t = 3.33 > 2.60 at 0.01 level of significance with '15' degrees of freedom
The null hypothesis is rejected
<u><em>Conclusion</em></u>:-
Accepted Alternative hypothesis H₁
The Claim that the true average is smaller than 5.5
<u><em></em></u>
This is a system of equations. We can solve it by recognizing the two linear equalities we've given to solve this equation.
First, let's start off by recognizing two variables: x and y. x will be our number of hard puzzles, and y will be our number of easy puzzles. We're given that the number of hard puzzles and easy puzzles sum to 50, so we can rewrite that as:
Next, we're given that the sum of the points gained from the hard puzzles (60x), and the number of points gained from the easy puzzles (30y), sum to 1950. We can rewrite that as:
Now, we have our two linear equations, and we must solve for the hard puzzles, so x. Solving for the hard puzzles means eliminating the easy puzzles from our systems, so we can multiply our first equation by 30, and subtract it from the first equation. This is a technique called elimination.
Since x=15, Tina has solved 15 hard puzzles.