A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates. Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories. At the .05 level of significance, is there sufficient evidence that the average calorie content of a 12-ounce can is greater than 120 calories? Assume that the number of calories per can is normally distributed.

Answers

Answer 1

Answer:

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let $\mu$ = average calorie content of a 12-ounce can.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, $H_A$ : $\mu$ > 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $(\bar X-\mu)/((s)/(√(n) ) )$ ~ $t_n_-_1$

where, $\bar X$ = sample average calories per can = 124 calories

s = sample standard deviation = 6 calories

n = sample of cans = 10

So, test statistics = $(124-120)/((6)/(√(10) ) )$ ~ $t_9$

= 2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

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(1) True or False? Explain your answer. The signs of the cosecant function will be the same as the sine function in each of the four quadrants.
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2-23 Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is inspected and found to be acceptable. At this point, what is the posterior probability that the lathe tool is properly adjusted?

Data taken from a random sample of 60 students chosen from the student population of a large urban high school indicated that 36 of them planned to pursue post-secondary education. An independent random sample of 50 students taken at a neighboring large suburban high school resulted in data that indicated that 31 of those students planned to pursue post-secondary education. Do these data provide sufficient evidence at the 5% level to reject the hypothesis that these population proportions are equal

Answers

Answer:

No, these data do not provide sufficient evidence at the 5% level to reject the hypothesis that these population proportions are equal.

Step-by-step explanation:

We are given that data taken from a random sample of 60 students chosen from the student population of a large urban high school indicated that 36 of them planned to pursue post-secondary education.

An independent random sample of 50 students taken at a neighboring large suburban high school resulted in data that indicated that 31 of those students planned to pursue post-secondary education.

Let $p_1$ = population proportion of students of a large urban high school who pursue post-secondary education.

$p_2$ = population proportion of students of a large suburban high school who pursue post-secondary education.

So, Null Hypothesis, $H_0$ : $p_1-p_2$ = 0 {means that these population proportions are equal}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq$ 0 {means that these population proportions are not equal}

The test statistics that would be used here Two-sample z proportionstatistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{(\hat p_1(1-\hat p_1))/(n_1)+(\hat p_2(1-\hat p_2))/(n_2) } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of students of a large urban high school who pursue post-secondary education = $(36)/(60)$ = 0.60

$\hat p_2$ = sample proportion of students of a large urban high school who pursue post-secondary education = $(31)/(50)$ = 0.62

$n_1$ = sample of students of a large urban high school = 60

$n_2$ = sample of students of a large suburban high school = 50

So, the test statistics = $\frac{(0.60-0.62)-(0)}{\sqrt{(0.60(1-0.60))/(60)+(0.62(1-0.62))/(50) } }$

= -0.214

The value of z test statistics is -0.214.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that these population proportions are equal.

The function f(x,y,z)equals2 x plus z squared has an absolute maximum value and absolute minimum value subject to the constraint x squared plus 2 y squared plus 3 z squaredequals16. Use Lagrange multipliers to find these values.

Answers

Answer:

Absolute maxima an minma both occured at $(25)/(3)$ .

Step-by-step explanation:

Given function is,

$f(x,y,z)=2x+z^2\hfill (1)$

subject to,

$x^2+2y^2+3z^2=16\hfill (2)$

Let $g(x,y,z)=x^2+2y^2=3z^2-16$

To find absolute maxima and absolute minima using Lagranges multipliers method consider $\lambda$ as the multipliers such that,

$\nabla f=\lambda \nabla g$

$\leftrightarrow (2, 0 ,2z )=\lambda (2x, 4y, 6z)$

on compairing both side we get,

$2z=6\lambda z\implies \lambda=(1)/(3)$

$4\labda y=0\implies y=0$

$2=2\lambda x\implies x=(1)/(\lambda)=3$

From (2),

$x^2+2y^2+3z^2=16$

$\implies 9+0+3z^2=16$

$\implies z=\pm\sqrt{(7)/(3)}$

Absolute maxima, at x=3, y=0, $z= \sqrt{(7)/(3)}$ is,

$|f(x,y,z)|_(max)=(2x+z^2)_(3,0,\sqrt{(7)/(3)})=(2*3)+(7)/(3)=(25)/(3)$

Absolute minima, at x=3, y=0, $z= -\sqrt{(7)/(3)}$ is,

$|f(x,y,z)|_(max)=(2x+z^2)_(3,0,-\sqrt{(7)/(3)})=(2*3)+(7)/(3)=(25)/(3)$

Hence the result.

Graph the line that passes through the given point and has the given slope m. (3,10); m=-(5)/(2)

Answers

Step-by-step explanation:

given a slope and a point that the line passes through you have 2 options

Option 1: Solve for the equation of the line so you can just use that to graph the line. In this scenario it would be y=(-5/2)x - (20/13)

Option 2: plot the given point and, based on the slope, plot the next point that it crosses. In this case the next point would be (5, 7). Then you can just draw a line using these 2 points.

David is having a cookout. Hot dogs and buns are sold based on the following quantities per package.Item
Amount Per Package
Hot dog buns
12
Hot dogs
10
A
David thought that he would have to buy 12 packages of hot dog buns and 10 packages of hot dogs to have one bun for each hot dog.
What is the LEAST amount of each David would need to buy to have an equal number of hot dogs and buns?
David should buy 2 packages of buns and 2 packages of hot dogs,
David should buy 6 packages of buns and 5 packages of hot dogs.
с David should buy 5 packages of buns and 6 packages of hot dogs,
D David should buy 22 packages of buns and 22 packages of hot dogs
B

Answers

Answer: Choice C) David should buy 5 packages of buns and 6 packages of hot dogs.

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Explanation:

Focus on the hot dog buns for now

1 package = 12 hot dog buns

2 packages = 24 hot dog buns (multiply both sides by 2)

3 packages = 36 hot dog buns (multiply original equation by 3)

We can see that the multiples of 12 are being listed. So we have

12, 24, 36, 48, 60, 72, 84, ...

as the possible number of hot dog buns we could get if we buy 1,2,3... packages.

The possible number of hot dogs we can get are

10, 20, 30, 40, 50, 60, 70, 80, ...

which are multiples of 10. Simply add 10 to each item to get the next one.

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Considering these two sets

12, 24, 36, 48, 60, 72, 84, ...

10, 20, 30, 40, 50, 60, 70, 80, ...

what is the lowest common multiple? That would be 60 since it is found in both lists and it is the smallest in common.

The LCM of 12 and 10 is 60.

If he wanted 60 hot dog buns, then 60/12 = 5 packages of buns is what he needs.

If he wanted 60 hot dogs, then he needs 60/10 = 6 packages of hot dogs.

Therefore, David should buy 5 packages of buns and 6 packages of hot dogs. The answer is choice C.

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Side note: a different way to find the LCM is to multiply 10 and 12 to get 10*12 = 120. Then we divide by the GCF 2 getting 120/2 = 60.

Toy company produces rubber balls that have a radius of 1.7 cm.A sphere has a radius of 1.7 centimeters.
What is the volume of one rubber ball? Round to the nearest hundredth of a centimeter.