Mathematics, 17.10.2020 20:01 Melleeroo

Question 1: The director of a green energy company is interested in comparing two different methods of installing solar light panels. An experiment is conducted with 31 technicians using the old method and the other 46 technicians using the new method. For the 31 technicians using the old method, the average time was 525 minutes with 47.7 standard deviation. For the 46 technicians using the new method, the average time was 520 minutes with 48.2 standard deviation. Conduct an analysis to determine whether there is a difference in the average time to complete the installation of the solar panels. Provide the test statistic value. Question 2:

The director of a green energy company is interested in comparing two different methods of installing solar light panels. An experiment is conducted with 39 technicians using the old method and the other 55 technicians using the new method.

For the 39 technicians using the old method, the average time was 582 minutes with 63.8 standard deviation.
For the 55 technicians using the new method, the average time was 542 minutes with 97.8 standard deviation.
Conduct an analysis to determine whether there is a difference in the average time to complete the installation of the solar panels. Provide the degrees of freedom.

Answers: 2

Show answers

Answers

Answer from: grayfaith16

Question 1

The test statistics is t = 0.44

The decision rule is

Fail to reject the null hypothesis

The conclusion

There is no sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels

Question 2

The degree of freedom is df = 92

The decision rule is

Reject the null hypothesis

The conclusion

There is sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels

Explanation:

Considering Question 1

Here we are told to provide the test statistics

From the question we are told that

The first sample size is n_1 = 31

The second sample size is n_ 2 = 46

The first sample mean is $\= x_1 = 525 \ minutes$

The first standard deviation is $\sigma_1 = 47.7$

The second sample mean is $\= x_2 = 520 \ minutes$

The second standard deviation is $\sigma_2 = 48.2$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 \ne 0$

Generally the degree of freedom is mathematically represented as

df = n_1 + n_2 -2

=> df = 31 + 46 -2

=> df = 75

Generally the test statistics is mathematically represented as

$t = \frac{(\= x_1 - \= x_2 )-0}{ \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} } }$

=> $t = \frac{( 525- 520 )-0}{ \sqrt{\frac{47.7^2}{31} + \frac{48.2^2}{46} } }$

=> t = 0.44

Let assume that the level of confidence is $\alpha = 0.05$

Generally the probability of t at a degree of freedom of is df = 75

P(t 0.44 ) = 0.33060124

Generally the p-value is mathematically represented as

p-value = 2 * P(t 2.398)

=> p-value = 2 * 0.33060124

=> p-value = 0.66120

From the value obtain we see that $p-value \alpha$ hence we fail to reject the null hypothesis

The conclusion is that there is no sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels

Considering Question 2

Here we are told to provide the degree of freedom

From the question we are told

The first sample size is n_1 = 39

The first sample mean is $\= x_1 = 582 \ minutes$

The first standard deviation is $\sigma_2 = 63.8$

The second sample size is n_ 2 = 55

The second sample mean is $\= x_2 = 542 \ minutes$

The second standard deviation is $\sigma_2 = 97.8$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 \ne 0$

Generally the degree of freedom is mathematically represented as

df = n_1 + n_2 -2

=> df = 39 + 55 -2

=> df = 92

Generally the test statistics is mathematically represented as

$t = \frac{(\= x_1 - \= x_2 )-0}{ \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} } }$

=> $t = \frac{( 582 - 542 )-0}{ \sqrt{\frac{63.8^2}{39} + \frac{97.8^2}{55} } }$

=> t = 2.398

Let assume that the level of confidence is $\alpha = 0.05$

Generally the probability of t at a degree of freedom of is df = 92

P(t 2.398 ) = 0.00925214

Generally the p-value is mathematically represented as

p-value = 2 * P(t 2.398)

=> p-value = 2 * 0.00925214

=> p-value = 0.0185

From the value obtain we see that $p-value < \alpha$ hence we reject the null hypothesis

The conclusion is that there is sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels

Answer from: Quest

757764

step-by-step explanation:

de77737dd

Answer from: Quest

here is your mark brainliest

Another question on Mathematics

Mathematics, 21.06.2019 20:00

How do you write something in scientific notation?

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Jason went to an arcade to play video games. he paid $2 for every 11 tokens he bought. he spent a total of $16 on tokens. which equation can be used to determine,t, the number lf tokens jason bought

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

According to the 2008 u.s. census, california had a population of approximately 4 × 10^7 people and florida had a population of approximately 2 × 10^7 people. which of the following is true? a. the population of california was approximately two times the population of florida. b. the population of florida was approximately twenty times the population of california. c. the population of florida was approximately two times the population of california. d. the population of california was approximately twenty times the population of florida.

Answers: 1

Answer

Mathematics, 22.06.2019 04:00

Ahealth-food producer has 250 samples of a new snack to distribute in the mall. the producer has to keep at least 50 samples for display in the health food for the product launch. how long will the samples last if consumers are taking the samples at a rate of 25 every hour

Answers: 2

Answer

You know the right answer?

Question 1: The director of a green energy company is interested in comparing two different methods...

Questions

Mathematics, 01.06.2021 15:20

I had 150 pencils at the start of the year. I now only have 120 pencils. What is the percent of change in the number of pencils? * * 20 %...