⚠️What is the slope of the line that passes through the points ( 4,9 ) and ( 14, 17)⚠️

A manufacturer uses production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standar

Arisa [49]

Answer:

$\chi^2 =\frac{17-1}{12.15} 22.09 =15.87$

Traditional method

We can find a critical value in the chi square distribution with df =16 who accumulates $\alpha/2 =0.05$ of the area on each tail and we got:

$\chi^2_{crit}= 7.962$

$\chi^2_{crit}=26.296$

Since the calculated value is between the two critical values we don't have enough evidence to conclude that the true deviation is NOT significantly different from 3.5 cm

Confidence level method

We can find the p value like this

$p_v =2*P(\chi^2 >15.87)=0.92$

Since the p value is higher then the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is NOT significantly different from 3.5 cm

Step-by-step explanation:

Data provided

$n=17$ represent the sample selected

$\alpha=0.1$ represent the significance

$s^2 =4.7^2 =22.09$ represent the sample variance

$\sigma^2_0 =3.5^2 =12.15$ represent the value to check

Null and alternative hypothesis

We want to verify if the new production method has lengths with a standard deviation different from 3.5 cm, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 = 12.15$

Alternative hypothesis: $\sigma^2 \neq 12.15$

The statistic for this case is given by:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

The degrees of freedom are:

$df =n-1= 17-1=16$

$\chi^2 =\frac{17-1}{12.15} 22.09 =15.87$

Traditional method

We can find a critical value in the chi square distribution with df =16 who accumulates $\alpha/2 =0.05$ of the area on each tail and we got:

$\chi^2_{crit}= 7.962$

$\chi^2_{crit}=26.296$

Since the calculated value is between the two critical values we don't have enough evidence to conclude that the true deviation is significantly different from 3.5 cm

Confidence level method

We can find the p value like this

$p_v =2*P(\chi^2 >15.87)=0.92$

Since the p value is higher then the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is significantly different from 3.5 cm

7 0

3 years ago

a class has ten girls and three boys. if the teacher randomly picks ten students,what is the probability that he will pick all g

grin007 [14]

Answer:

10/13

Step-by-step explanation:

You will first add all the students the mentioned which gives you 13 then since they ask what is the probability it the teacher would pick girls. You know there's 10 girls and 3 boys so it would be 10/13.

7 0

2 years ago

A hospital’s financial reimbursement payor mix indicates 35% of the patients have Medicare and 15% have Medicaid. Of those who h

Damm [24]

Using conditional probability, it is found that there is a 0.035 = 3.5% probability that a hospital patient has both Medicare and Medicaid.

<h3>What is Conditional Probability?</h3>

<em>Conditional probability</em> is the <u>probability of one event happening, considering a previous event</u>. The formula is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem, the events are:

Event A: Patient has Medicare.

Event B: Patient has Medicaid.

For the probabilities, we have that:

35% of the patients have Medicare, hence $P(A) = 0.35$ .

Of those who have Medicare, there is a 10% chance they also have Medicaid, hence $P(B|A) = 0.1$ .

Then, applying the <em>conditional </em>probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.1 = \frac{P(A \cap B)}{0.35}$

$P(A \cap B) = 0.35(0.1)$

$P(A \cap B) = 0.035$

0.035 = 3.5% probability that a hospital patient has both Medicare and Medicaid.

You can learn more about conditional probability at brainly.com/question/14398287

4 0

2 years ago

Eliminate the decimal from 0.15/0.003

Lera25 [3.4K]

The correct answer is 50

8 0

2 years ago

Why did the math teacher open a window company?

umka2103 [35]

A math teacher opened a window company because he loves seeing shapes or geometrical polygons such as rectagles, squares or quadrilaterals in general as well as triangles in his works. Of course, the math teacher is already familiar with these shapes and how to calculate the angles in between.

4 0

3 years ago

Read 2 more answers