The glacier moves 5 centimeters in 8 days. How many days does it take the glacier to move 1 centimeter?

The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba

blsea [12.9K]

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

$\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537$

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

$\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712$

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

$H_0: \mu_1 - \mu_2 = 0$

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

$H_1: \mu_1 - \mu_2 \neq 0$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that $\mu = 0$

From the two samples:

$X = \mu_1 - \mu_2 = 1276 - 1439 = -163$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144$

Test statistic:

$z = \frac{X - \mu}{s}$

$z = \frac{-163 - 0}{77.3144}$

$z = -2.11$

The test statistic is z = -2.11.

7 0

3 years ago

Can you tell me how to factorise 6b+24bc

Kamila [148]

When we factorise an expression, we are looking for simple factors that multiply to get the original expression. Usually it is very natural to factorise something like a quadratic in x. For example:

x^2 + 3x + 2 = (x+1)(x+2)

But there are other situations where factorisation can be applied. Take this quadratic:

x^2 - 9x = x(x-9)

This second example is closer to the question in hand. Just like x was a common factor to both x^2 and -9x, we are looking for a common factor to both 6b and 24bc. The common factor is 6b.

Hence 6b + 24bc = 6b(1 + 4c).

I hope this helps you :)

3 0

2 years ago

Read 2 more answers

Brad says that if a second number is 125% of the first number than the second number must be 75% of the second number is he corr

elena-s [515]

Answer:

Incorrect.

Step-by-step explanation:

Let, the first number is x, and the second number is y. Given, the second number is 125% of the first number. So, the equation will be

y = 1.25 x

Or, y= 5/4x

Now, multiplying it with 4/5, we get, x= 4/5y

Or, x= 0.80 y

But, Brad is saying the first number must be 75% of the second number. But here we see that the first number is 80% of the second number. That's why Brad is incorrect.

5 0

2 years ago

Jossline rented a bicycle while she was on vacation. She paid a flat rental fee of $55 plus

Nat2105 [25]

Answer: 123/8.50

Step-by-step explanation:

6 0

3 years ago

Express 3cm: 3m in the ratio of its simplest form

Dmitry_Shevchenko [17]

Answer:

1cm:100cm

Step-by-step explanation:

You have to convert the ratio into the same unit (I chose cm). If there are 100cm in a metre, there will be 300cm in 3m.

That leaves you with the ratio 3cm:300cm. To simplify, divide both sides by three leaving you with 1cm:100cm

3 0

3 years ago

Read 2 more answers