A marine biologist wants to test the effect of water temperature on the length of time sea otters can remain under water during a dive. He gathers data on randomly selected dives by 7 different otters, recording dive duration (in seconds) and water temperature (in degrees Celsius). A computer regression analysis of his data is given below. Assume all conditions for inference for slope have been met.

Predictor Coef SE coef T P
Constant 52.789 5.257 10.04 0.000
Water temp 3.3684 0.4216 7.990 0.002
S= 5.557 R- Sq= 92.7% R-Sq(adj)= 91.3%

Required:
What is the estimate of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship?

Answer:

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

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

Subtraction of normal variables:

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

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.

This means that [tex]\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626[/tex]

In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.

This means that [tex]\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs[/tex]

[tex]M = 1.645*0.1314 = 0.22[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N

The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

Answer:

true

false

true

false

true

false

Step-by-step explanation:

Bert, Camille, and Etsuko.

Answer:

Bert, Camille, and Etsuko has the solution as x = 4.

Step-by-step explanation:

Bert:

2x - 9 = -1

Camille:

-2x + 12 = 4

Etsuko

[tex]2(x - 10) = - 12[/tex]

Answer: 3n - 12

Product means multiplication. So the 3 and n are being multiplied. If 12 is less than, then that means it is being subtracted from 3n, not the other way around.

Answer:

178.2 ft

Step-by-step explanation:

[tex] \sin(60) = \frac{x}{200} \\ \frac{ \sqrt{3} }{2} = \frac{x}{200} \\ x = 100 \times \sqrt{3}[/tex]

So,

[tex]h = 5 + x = 5 + 100 \times \sqrt{3} = 178.2[/tex]

Answer:

4/5 is the slope

Answer:

(-5,-4) or (-4, -5)

Step-by-step explanation:

Answer:

you need more information to answer this, it's either 84 or 56 since it's in acute angle. looks closer to 84

Answer:

Step-by-step explanation:

19 of 22 participants (86.36%) from the high-power posing group took a gambling risk to double their money, while 12 of 20 (60%) from the low-power posing group took the gambling risk. Use a calculator tool from Module 10 to determine the p-value associated with the hypothesis test examining if there is a statistically significant difference between the proportion of people willing to take risks in the two groups. Round to 3 decimal places

H0 : P1 - P2 = 0

H1 : P1 - P2 ≠ 0

P1 = 0.8636

P2 = 0.6

q1 = 1 - P1 = 0.1364

q2 = 1 - P2 = 0.4

Tstatistic = (p1 - p2) ÷ √(p1q1)/n1 + (p2q2)/n2]

Tstatistic = (0.8636-0.6) ÷ √0.01735432]

Tstatistic = 0.2636 ÷ 0.1317357

Test statistic = 2.0009761

Test statistic = 2

The Pvalue from t statistics :

Tscore = 2 ; df = 20 + 22 - 2 = 40

Answer:

Summary. The Addition Property states that: a=bis equivalent toa+c=b+cora−c=b−c Basically, whatever you do to one side of the equal sign, you have to do to the other side.

Hope this helps!!! :)

Answer:

2,3,4, and 5

Step-by-step explanation:

#1

So all are positive

#2

In Q3

Hence all are negative

#4

Yes anything left to or bottom to zero us negative

#6

option A,B,D,F are correct

Answer:

Step-by-step explanation:

n+37=180

n=180-37=143°

Answer:

B) 143°

Step-by-step explanation:

Since n° is supplementary to 180°, then n°=180°-37°=143°.

Answer:

200

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Answer:

Hi how are you doing today Jasmine

Answer:

Step-by-step explanation:

Answer:

40.4

Step-by-step explanation:

Use the formula if you have one, (AS = 2Ab (a+b+c)h)

Then apply.

Answer:

xxyy2578

Step-by-step explanation:

Answer:

15 ml

Step-by-step explanation:

Find the volume of the tank which is 1.8m*0.6m*0.5m=0.54m^3

For every 0.18m^3,5ml of treatment is added,what of 0.54m^3

(0.54m^3*5ml)/(0 18m^3)=15ml

Given:

The point (5,-2) is translated 3 units to the left.

To find:

The new location of the point.

Solution:

If a point is translated 3 units to the left, then

[tex](x,y)\to (x-3,y)[/tex]

Using this rule of translation, we get

[tex](5,-2)\to (5-3,-2)[/tex]

[tex](5,-2)\to (2,-2)[/tex]

Therefore, the new location of the point is (2,-2). Hence, the correct option is C.

Answer:

450 students

Step-by-step explanation:

Answer:

n/4-6

Step-by-step explanation:

n/4-6

This is the expression because we need to divide n by 4 and subtract 6

The number is 68

68 divided by 4= 17

17-6=11

Answer:

I think it's 64 in

I hope it's helps you

This is in contrast to theoretical probability where it's what we think would happen, or predict to happen.

For example, the theoretical probability of getting heads on a coin is 1/2 = 0.50 = 50%. If you flip a coin say 1000 times and get 400 heads, then the empirical or experimental probability of getting heads is 400/1000 = 0.40 = 40%. The experimental probability is what actually happens when you do the experiment. The theoretical probability is what you predict what would happen given some list of assumptions and rules about the object.

According to the law of large numbers, the experimental probability should get closer and closer to the theoretical one assuming the theoretical probability has been calculated properly (and all assumptions are correct). If we got say 475 heads instead of 400, then we might have fairly good evidence that we have a fair coin (since 475/1000 = 0.475 is fairly close to 0.500); however, if we got something like 300 heads then we might suspect that the coin is biased toward tails than it is toward heads. The more trials you do, the better a picture you can get of it.

Answer: 10%

Step-by-step explanation:

Since the shopkeeper purchased 60 pencil boxes for 4,500, he purchased them at the rate of:

= 4500 / 60

= 85 per pencil box

If the shopkeeper sold them at the rate of 4,125 for 50 pencil boxes, then he sold them at the rate of:

= 4125 / 50

= 82.50 per pencil box.

Therefore the percentage profit will be:

= Gain / Cost price × 100

= (82.50 - 75) / 75 × 100

= 7.5/75 × 100

= 10%

Use the binomial theorem:

[tex]\displaystyle (2x-9)^5 = \sum_{k=0}^5 \binom5k (2x)^{5-k}(-9)^k = \sum_{k=0}^5 \frac{5!}{k!(5-k)!} 2^5 \left(-\frac92\right)^k x^{5-k}[/tex]

The x ³ terms occurs for 5 - k = 3, or k = 2, and its coefficient would be

[tex]\dfrac{5!}{2!(5-2)!} 2^5 \left(-\dfrac92\right)^2 = \boxed{6480}[/tex]

Answer:

[tex]1 \to 22 \to 0.176[/tex]

[tex]2 \to 13 \to 0.104[/tex]

[tex]3 \to 18 \to 0.144[/tex]

[tex]4 \to 29 \to 0.232[/tex]

[tex]5 \to 37 \to 0.296[/tex]

[tex]6 \to 6 \to 0.048[/tex]

Step-by-step explanation:

Given

[tex]n = 125[/tex]

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

[tex]Pr = \frac{Frequency}{n}[/tex]

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

[tex]Pr(2) = \frac{13}{125} = 0.104[/tex]

[tex]Pr(4) = \frac{29}{125} = 0.232[/tex]

[tex]Pr(6) = \frac{6}{125} = 0.048[/tex]

When the frequency is to be calculated, we use:

[tex]Pr = \frac{Frequency}{n}[/tex]

[tex]Frequency = n * Pr[/tex]

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

[tex]Frequency(3) = 125 * 0.144 = 18[/tex]

[tex]Frequency(5) = 125 * 0.296 = 37[/tex]

For roll of 1 where the frequency and the probability are not known, we use:

[tex]Total \ Frequency = 125[/tex]

So:

Frequency(1) added to others must equal 125

This gives:

[tex]Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125[/tex]

[tex]Frequency(1) + 103 = 125[/tex]

Collect like terms

[tex]Frequency(1) =- 103 + 125[/tex]

[tex]Frequency(1) =22[/tex]

The probability is then calculated as:

[tex]Pr(1) = \frac{22}{125}[/tex]

[tex]Pr(1) = 0.176[/tex]

So, the complete table is:

[tex]1 \to 22 \to 0.176[/tex]

[tex]2 \to 13 \to 0.104[/tex]

[tex]3 \to 18 \to 0.144[/tex]

[tex]4 \to 29 \to 0.232[/tex]

[tex]5 \to 37 \to 0.296[/tex]

[tex]6 \to 6 \to 0.048[/tex]

Answer:

3

Step-by-step explanation:

You can put 3 in 9 three times