Help with 5 and 6 please !! (13 points!!)
2 answers:
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Answer:
The test statistic is z = -2.11.
Step-by-step explanation:
Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Group 1: Sample of 35, mean of 1276, standard deviation of 347.
This means that:
Group 2: Sample of 35, mean of 1439, standard deviation of 298.
This means that:
Test if there is a difference in productivity level.
At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So
At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that
From the two samples:
Test statistic:
The test statistic is z = -2.11.
Answer:
Hence measure of arc ACD and arc AC are 340 degrees and 160 degrees respectively.
Step-by-step explanation:
Given:
A Circle with p as center and AB and CD as 2 diameters for a circle.
To Find:
Measure of ACD, and arc AC when arc AD is 20 degrees.
Solution:
<em>As we know that , Diameter is biggest chord which passes through center of circle,</em>
<em>Hence it divides the circle into two equal parts and making center as midpoint of it</em> .
(Refer the attachment)
angle APD=20 degree or arc AD=20 degree.
So AB as diameter ,so arc DB=160 degree or BPD=160 degree as A-B-P are
and angle APD and BPC are vertical opposite angles so they are congruent BPC=20 degree
Now,
points A,C,B,D,A makes circle which measures 360 degrees.
to find ACD
measure of ACD=360-(meaure of arc AD or angle APD)
=360-20
=340 degree.
Now arc AC,
as AB is diameter with p as midpoint ,A-P-B
arc APB=180 and arc BC=20 or angle BPC=20 degrees.
For measure of arc AC= measure of arc APB- arc BC
arc AC=180-20 degrees.
arc AC=160 degrees.
