MATHEMATICS
COLLEGE

(A) Reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.

(B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.

(C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours.

(D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean battery life of the smartphone is not equal to 20 hours.

Answer:

Answer:

(B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours.

(C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours.

Step-by-step explanation:

1) Data given and notation

represent the battery life 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)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean battery life is less than 20 :

Null hypothesis:

Alternative hypothesis:

Since we don't know the population deviation, 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".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

4) P-value

First we need to calculate the degrees of freedom given by:

Since is a one-side lower test the p value would be:

5) Conclusion

If we compare the p value and the significance level given we see that \alpha" alt="p_v>\alpha" align="absmiddle" class="latex-formula"> so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the average battery life it's not significantly different less than 20 hours at 5% of signficance. If we analyze the options given we have:

(A) Reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours. FALSE, we FAIL to reject the null hypothesis.

(B) Fail to reject the null hypothesis that the true population mean battery life of the smartphone is equal to 20 hours. TRUE, we fail to reject the null hypothesis that the mean would be 20 or higher .

(C) There is not enough evidence at the α=0.05 level of significance to suggest that the true population mean battery life of the smartphone is less than 20 hours. TRUE, we FAIL to reject the null hypothesis that the mean is greater or equal to 20 hours, so we reject the alternative hypothesis that the mean is less than 20 hours.

(D) There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean battery life of the smartphone is not equal to 20 hours. FALSE the claim is not that the mean is different from 20. The real claim is: "Javier believes the mean battery life is less than 20 hours".

MIDDLE SCHOOL

15 PTS!!!!!!!!!! Which statement is true about the meaning of the equation

2 = 3 x 2/3

act fast!!!!!!

Answer:

C.

Step-by-step explanation:

the number two is 3 times the size of 2/3

2 = 3 * 2/3

MIDDLE SCHOOL

What is the approximate volume of a cone with a height of 12in. and radius of 9 in. ? Use 3.14 to approximate pi, and express your final answer to the nearest hundredth. Enter your answer in the box.

__in^3

Answer:

V=1017.36in^3

Step-by-step explanation:

Volume of a cone is given by

V=πr^2h/3

Given that, r=9in, h=12in

Given that π=3.14

V=3.14×9×9×12/3

Then,

V=1017.36in^3.

Now, to the nearest hundredth

V=1017.36in^3

Answer:

1017.88

Step-by-step explanation:

that is the answer if you use the volume of cone equation

HIGH SCHOOL

Express 125 = 5x as a logarithmic equation

I guess the original expression is 125 = 5^x

If you apply logarithms to both sides, you get:

log (125) = x * log (5) x = log (125) / log(5)

Given that 125 is 5^3

you can simplify to

x = log (5^3) / log(5) = 3 log (5) / log (5) = 3 * 1 = 3

There you have the expression as a logarithmic equation and the solution of the equation.

If you apply logarithms to both sides, you get:

log (125) = x * log (5) x = log (125) / log(5)

Given that 125 is 5^3

you can simplify to

x = log (5^3) / log(5) = 3 log (5) / log (5) = 3 * 1 = 3

There you have the expression as a logarithmic equation and the solution of the equation.

Answer:The answer is log5 125 = x

Step-by-step explanation:

COLLEGE

Evaluate i^i. Is this real, imaginary or neither?

Answer:

The number is a real number.

Step-by-step explanation:

First, let us recall the exponential form of a complex number: if it can be written as

where and is the argument of .

Also, let us recall Euler's formula: if x is a real number

.

Using this, we have

.

So, if we elevate both sides to

.

But, .

Therefore, which is a real number.