Find the missing divisor: 9.21 divide ____= -1.535
1 answer:
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Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis.
Step-by-step explanation:
Data given and notation
Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5
We can begin calculating the sample mean given by:
And the sample deviation given by:
And we got:
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis.
Step-by-step explanation:
Given : A rectangle 4 x 8 , a semicircle
Diagonal intersecting semicircle
To Find :Area of red part
<h3>Solution:</h3>Angle AC make AB α = ∠BAC
tan α = BC/AB = 4/8 = 1/2
=> α = 26.565°
∠ECA = ∠BAC = α
EC = EF = 4
=> ∠CEF = 180° - 2α
∠AED = 45° as AE is diagonal of Square of side 4
=> ∠AEF + 180° - 2α + 45° = 180°
=> ∠AEF = 2α - 45° = 8.13°
in Left side area between square and circle is split in 2 Equal parts
(1/2) area - area AFG = area of Red part
in Left side area between square and circle = 4² - (1/4)π4²
= 3.4336 sq unit
half = 1.7168 sq unit
Now find area AFG = area ΔAEF - sector EGF
area ΔAEF
AE = 4√2 , EF = 4 angle = 8.13°
area ΔAEF = (1/2) 4√2 * 4 sin 8.13° = 1.6 sq unit
area sector EGF = (8.13/360)π4² = 1.135 sq unit
area AFG = 1.6 - 1.135 = 0.465 sq unit
Area of Red part = 1.7168 - 0.465 sq unit
= 1.2518 sq unit
= 1.252 sq unit
= 1.25 sq unit.
Hope this helps!!
