The Pythagorean theorem is true for some right triangles, but not all.
2 answers:
<h2>Answer:</h2>
The given statement is a FALSE statement.
<h2>Step-by-step explanation:</h2><u>Pythagorean Theorem--</u>
It states that if a and b are two legs of a right angled triangle and c is the hypotenuse of the right angled triangle then,
The square of hypotenuse is equal to the sum of the square of the two legs of the triangle.
i.e.
This theorem is true for all the right triangle.
Option: B is the correct answer.
B. False
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Answer:
1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).
2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.
3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.
Step-by-step explanation:
1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.
2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.
The null hypothesis state that there is not significant difference from 519.
The critical value for a significance level of 5% is z=1.96.
3) The claim is that the true mean is not 519 ml.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=16.
The sample mean is M=522.
The standard deviation of the population is known and has a value of σ=6.
We can calculate the standard error as:
Then, we can calculate the z-statistic as:
This test is a two-tailed test, so the P-value for this test is calculated as:
As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the true mean is not 519 ml.
For x=3, the denominator is equal to 0 and you can't divide by 0.