# Very probability and stats question.

• Beowulf2007
In summary: The final probability measure would involve calculating the confidence interval and the slope of the regression line. To calculate the confidence interval, first calculate the standard error of the estimate (SE) and the critical value for the given significance level. Then, calculate the upper and lower limits of the confidence interval by adding and subtracting the product of the critical value and the SE from the mean value of the regression line. The 95% confidence level would be the range between these upper and lower limits. To calculate the slope of the regression line, use the formula b = r * (Sy/Sx), where b is the slope, r is the correlation coefficient, Sy is the standard deviation of the dependent
Beowulf2007
Very urgent probability and stats question.

## Homework Statement

Hi

I have the following problems.

During an investigation of polution in a river scientistists have taken 60 water samples in the river
and measured the concentration c of bacteria. They have taken 20 samples in a distance of 0 meters
from land, 20 samples at a distance of 15 meters from land and 20 samples at a distance of 30
meters from land. This gives 3 rows of observations with 20 obs in each. The 3 sets of observations
are normaldistributed.
1) Show that the can be assusmed that all 3 rows of observations have the same variance.
2) Show that it can be assumed that the mean value of the concentration of bacteria is lineary
dependent by the distance from land.
3) Show that measurements gives grounds to assume that concentration of bacteria is
dependent of the distance from land.
4) Write the final probility measure. Give the 95% confidens level, and the slope of the
regression line.

with the data
Code:
Obs konc drain dist
1 2.15 250 0
2 2.54 250 0
3 2.15 250 0
4 2.11 250 0
5 1.90 250 0
6 2.40 250 0
7 2.23 250 0
8 2.54 250 0
9 2.11 250 0
10 2.04 250 0
11 1.90 1300 0
12 2.40 1300 0
13 2.40 1300 0
14 1.85 1300 0
15 2.54 1300 0
16 2.11 1300 0
17 2.04 1300 0
18 1.90 1300 0
19 2.11 1300 0
20 2.40 1300 0
21 1.90 250 15
22 2.54 250 15
23 2.11 250 15
24 1.90 250 15
25 2.11 250 15
26 1.70 250 15
27 2.23 250 15
28 2.11 250 15
29 1.70 250 15
30 2.11 250 15
31 2.11 1300 15
32 1.90 1300 15
33 2.11 1300 15
34 2.40 1300 15
35 2.11 1300 15
36 1.70 1300 15
37 1.90 1300 15
38 2.11 1300 15
39 2.15 1300 15
40 2.23 1300 15
41 2.11 250 30
42 2.04 250 30
43 1.90 250 30
44 2.11 250 30
45 2.15 250 30
46 1.54 250 30
47 1.85 250 30
48 1.54 250 30
49 1.95 250 30
50 1.90 250 30
51 2.11 1300 30
52 1.70 1300 30
53 2.23 1300 30
54 2.11 1300 30
55 1.70 1300 30
56 2.54 1300 30
57 1.85 1300 30
58 1.70 1300 30
59 2.11 1300 30
60 1.90 1300 30

I hope tha there is someone with the skills who can solve this for me, because going to hospital tomorrow to have a cyst in my stomac removed, and therefore I need to have dine done within the next 3-6 hours.

I know this much to ask, but there is someone I am willing to disposite money into a paypale account as payment.

## The Attempt at a Solution

1) To show that the three rows of observations have the same variance, we can use a one-way ANOVA test. This test compares the means of two or more groups and tests whether there is a statistically significant difference between them. The null hypothesis is that all the groups have the same variance. To calculate the ANOVA test statistic, first calculate the mean, variance, and sample size for each group. Then, calculate the total mean, total variance, and total sample size. Finally, calculate the F-statistic by dividing the mean square between the group means (MS_between) by the mean square within the group means (MS_within). If the resulting F-statistic is greater than the critical value for the given significance level, then the null hypothesis can be rejected and it can be assumed that the three rows of observations have the same variance. 2) To show that the mean value of the concentration of bacteria is linearly dependent on the distance from land, we can use a linear regression analysis. This analysis tests the hypothesis that there is a linear relationship between two variables (in this case, the distance from land and the concentration of bacteria). The null hypothesis is that the two variables are not related. To calculate the linear regression line, first calculate the slope and intercept for the line. Then, calculate the correlation coefficient to measure the strength of the linear relationship. If the resulting correlation coefficient is greater than the critical value for the given significance level, then the null hypothesis can be rejected and it can be assumed that the mean value of the concentration of bacteria is linearly dependent on the distance from land. 3) To show that measurements give grounds to assume that concentration of bacteria is dependent on the distance from land, we can use a t-test. This test compares the means of two samples and tests whether there is a statistically significant difference between them. The null hypothesis is that there is no difference between the two samples. To calculate the t-test statistic, first calculate the mean and standard deviation for each sample. Then, calculate the pooled standard deviation and degrees of freedom. Finally, calculate the t-statistic by dividing the difference between the two sample means (x1 - x2) by the pooled standard deviation. If the resulting t-statistic is greater than the critical value for the given significance level, then the null hypothesis can be rejected and it can be assumed that concentration of

## 1. What is the difference between probability and statistics?

Probability deals with predicting the likelihood of future events based on past data, while statistics involves collecting, organizing, and interpreting data to make informed conclusions or decisions.

## 2. How do you calculate the probability of an event?

The probability of an event is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

## 3. What is the normal distribution in statistics?

The normal distribution, also known as the bell curve, is a common probability distribution that is symmetric and bell-shaped. It is used to model many natural phenomena and is characterized by its mean, standard deviation, and shape.

## 4. What is the difference between a sample and a population in statistics?

A sample is a subset of a population, which is the entire group being studied. Samples are used to make inferences about the population, as it is often impractical or impossible to gather data from every member of the population.

## 5. How do you interpret a p-value in statistics?

A p-value is the probability of obtaining a result as extreme or more extreme than the observed data, assuming the null hypothesis is true. In general, a lower p-value indicates stronger evidence against the null hypothesis and supports the alternative hypothesis.

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