Mathematics, 17.12.2020 04:30 bdbsjncns

It is known that a particular laboratory task takes the average person 2.5 seconds. A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their meantime was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude (use the .05 level)?

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Answer from: zionlopez543

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that older people are slower

Step-by-step explanation:

From the question we are told that

The average time taken is $\mu = 2.5 \ seconds$

The sample size is n = 30

The sample mean is $\= x = 2.7 \ seconds$

The standard deviation is $\sigma = 1.4 \ seconds$

The null hypothesis is $H_o: \mu = 2.5$

The alternative hypothesis is $H_a : \mu 2.5 \ seconds$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }$

=> $z = \frac{ 2.7 -2.5 }{ \frac{1.4}{ \sqrt{30} } }$

=> z = 0.7825

From the z table the area under the normal curve to the right corresponding to 0.7825 is

p-value = P(Z 0.7825 ) = 0.21696

So from the question we see that the $p-value \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that older people are slower

Answer from: Quest

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

What is the length of the unknown leg in the right triangle ?

Answer from: Quest

theres no picture: /

step-by-step explanation:

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