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andrew-mc [135]
3 years ago
10

A simple random sample of 32 men from a normally distributed population results in a standard deviation of 12.9 beats per minute

. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normalâ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute.
Required:
Identify the null and alternative hypotheses.
Mathematics
1 answer:
krok68 [10]3 years ago
4 0

Answer:

Null Hypothesis, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute

Alternate Hypothesis, H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

Step-by-step explanation:

The null hypothesis is basically the problem statement i.e

Pulse rates of men have a standard deviation equal to 10 beats per minute

Hence, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute

The alternate hypothesis will contradict or negate the null hypothesis i.e

H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

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Ivan

Answer:

\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

<u>Given</u><u> </u><u>:</u><u>-</u>

• \sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}

<u>To</u><u> </u><u>Prove</u><u> </u><u>:</u><u>-</u><u> </u>

•\sf\implies cos2A =\dfrac{\sqrt3}{2}

<u>Proof </u><u>:</u><u>-</u><u> </u>

We know that ,

\sf\implies cos2A = 1 - 2sin^2A

Therefore , here substituting the value of sinA , we have ,

\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2

Simplify the whole square ,

\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8}

Add the numbers in numerator ,

\sf\implies cos2A =  1-2\times \dfrac{4-2\sqrt3}{8}

Multiply it by 2 ,

\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4}

Take out 2 common from the numerator ,

\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4}

Simplify ,

\sf\implies cos2A =  1 -\dfrac{ 2-\sqrt3}{2}

Subtract the numbers ,

\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2}

Simplify,

\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }

Hence Proved !

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In order to design an experiment, as the data is completely random and unknown, thus the experiment is designed such that the probability of individual option is 1/6.

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Answer:

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3 years ago
Read 2 more answers
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