Solve the formula for the specified variable

Consider the following hypothesis test: H0: LaTeX: \mu_1-\mu_2=0μ 1 − μ 2 = 0 Ha: LaTeX: \mu_1-\mu_2\ne0μ 1 − μ 2 ≠ 0 The follow

Pavel [41]

Answer:

$z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53$

Step-by-step explanation:

Data given and notation

$\bar X_{1}=104$ represent the mean for the sample 1

$\bar X_{2}=106$ represent the mean for the sample 2

$\sigma_{1} =8.4$ represent the population standard deviation for the sample 1

$\sigma_{2}=7.6$ represent the population standard deviation for the sample 2

$n_{1}=80$ sample size for the group 1

$n_{2}=70$ sample size for the group 2

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0: $\mu_{1}-\mu_{2} =0$

H1: $\mu_{1} -\mu_{2} \neq 0$

If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

And with this we can replace in formula (1) like this:

$z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53$

7 0

3 years ago

FIND THE VOLUME

galben [10]

1. The figure is a prism: V = lwh = (12.1)(5.3)(4.2) = 269.3 cu. cm.

2. The figure is also a prism but the base is triangular: V = 1/2*b*h*l = 1/2*(13)*(sqrt(3)/2*13)*24 = 1756.3 cu. yd.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

8 0

3 years ago

What is 43.586 rounded to the nearest hundredth

USPshnik [31]

The answer is 43.590.

5 0

3 years ago

Read 2 more answers

The balance on a credit card, that charges a 15.5%APR interest rate, over a 1 month period is given inthe following table:Days 1

Karo-lina-s [1.5K]

First step is to get the average daily balance.

Take the sum of each day's balances.

If a payment has been made, the sign will be negative.

From Days 1 - 5 :

Day 1 = $200

Day 2 = $200

...

Day 5 = $200

That's $200 x 5 days = $1000

From Days 6 - 20 :

Day 6 = $350

Day 7 = $350

...

Days 20 = $350

That's $350 x 15 days = $5250

From Days 21 - 30 :

Day 21 = $150

Day 22 = $150

...

Day 30 = $150

That's $150 x 10 days = $1500

A total of :

$1000 + $5250 + $1500 = $7750

Now divide this total to the number of days to get the ADB or Average Daily Balance.

$\text{ADB}=\frac{7750}{30}=258.33$

Next Step is to calculate for the finance charge using the formula :

$\text{Charge}=\text{ADB}\times r\times d$

where ADB is the average daily balance

r is the interest rate per day

d is the number of days or period given

From the problem, APR is 15.5%, it means that we need to divide the APR by 365 days.

So r = 0.155/365 = 0.000425

And we have d = 30 days

The charge will be :

Charge = 258.33 x 0.000425 x 30 = $3.29

The answer is $3.29

5 0

1 year ago

Write an equivalent ratio for 7 to 9?

Molodets [167]

14:18 is an equivalent ratio!

8 0

3 years ago