The Wall Street Journal recently published an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" 24% of the men compared to 62% of the women responded "Yes". Suppose that 150 women and 200 men were interviewed.
a) What are the null and alternative hypotheses that The Wall Street Journal should test in order to show that its claim is true?
b) For a 0.01 level of significance, what is the critical value for the rejection region?
c) What is the value of the test statistic? (hint: you need to find pbar)
d) What is the p-value of the test?
e) What conclusion should be reached?

Answer:

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case the confidence interval obtained is: (23.6 ; 27.3)

And the best interpretation would be:

We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n=94 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case the confidence interval obtained is: (23.6 ; 27.3)

And the best interpretation would be:

We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3

Answer:

A) Null hypothesis: H0: p = 0.398

Alternative hypothesis: H0: p < 0.398

B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.

C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.

Step-by-step explanation:

A) The null and alternative hypotheses are given below:

From the given information, the claim is that the proportion of students who enroll in her institution have a lower completion rate. This is representing the alternative hypothesis. Thus

Null hypothesis:

H0: p = 0.398

Alternative hypothesis:

H0: p < 0.398

B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.

C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.

Two consecutive odd integers are [tex]2k+1[/tex] and [tex]2k+3[/tex], for some integer [tex]k[/tex].

Their product is [tex](2k+1)(2k+3)=4k^2+8k+3[/tex].

Twice their sum is [tex]2(2k+1+2k+3)=2(4k+4)=8k+8[/tex]

Since the product is 1 less than twice the sum, we have

[tex]\underbrace{4k^2+8k+3}_{\text{the product}}=\underbrace{8k+8}_{\text{twice the sum}}-1[/tex]

So, we have

[tex]4k^2-4=0 \iff 4k^2=4 \iff k^2=1 \iff k=\pm 1[/tex]

If [tex]k=1[/tex], the integers are 3 and 5

If [tex]k=-1[/tex], the integers are -1 and 1.

In both cases, in fact, we have:

Answer:

[tex]25.00\geq 3.50p[/tex]

Step-by-step explanation:

since you have $25.00, you can only spend up to that much money, so it will have to be less than or equal to , and since p = slices of pizza, you multiply that by 3.50 to know how much you can buy.

hope this helps :)

Answer:

$3.5p<=$25.00

Step-by-step explanation:

If you only have $25.00 to spend on pizza it can not exceed that limit, so your total amount needs to be more than or equal to money the pizza slices cost

Answer:

Step-by-step explanation:

£21000/7=3000

I got seven by adding 2 and 5

3000 times 2=6000

3000 times 5 = 15000

6000:15000

6000 for the venue

15000 for the band

The amount of money the venue makes from the ticket sales is  £6000.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

The amount the venue makes =  2/7 x 21000 = £6000

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Final answer:

The smallest perimeter for a rectangle with an area of 36 square inches is 24 inches, and the dimensions that achieve this are those of a square, specifically 6 inches by 6 inches.

Explanation:

The smallest perimeter of a rectangle with an area of 36 square inches is achieved when the rectangle is a square because the sides are equal, and a square minimizes the perimeter for a given area. The formula for the area of a square is area = side², so if we have an area of 36 square inches, the side length of the square is √36, which equals 6 inches. Using this side length, we can calculate the perimeter of the square, which is perimeter = 4 × side, giving us a perimeter of 6 inches × 4, which is 24 inches.

The smallest perimeter we can have is 24 inches, and the dimensions of the rectangle (in this case, a square) that give us this smallest perimeter are 6 inches by 6 inches.

Answer:

320

Step-by-step explanation:

2/5 = .4

800 * .4 =320

Answer:

2 is the scale factor

100% increase/growth

Step-by-step explanation:

y = a × (b^t)

b is scale factor

b = 2 means 200% of tte previous value

100% growth

Answer:

its c The number of leaves is multiplied by 2 each week.

Step-by-step explanation:

because i just did it

Answer:

it can be written in eqn form as

x-8=>17

or,x=>25

Answer:

x-8 ≥17

If you need to find x, Add 8 on both sides

x ≥25

Hope this helped

Answer:

(0.0657,0.0943)  is the 90% confidence interval for the population proportion of visitors that click on the advertisement.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 978

Percentage of users that clicked on advertisement = 8%

Sample proportion:

[tex]\hat{p} = 0.08[/tex]

90% Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.645[/tex]

Putting the values, we get:

[tex]0.08\pm 1.645(\sqrt{\dfrac{0.08(1-0.08)}{978}})\\\\= 0.08\pm 0.0142\\\\=(0.0658,0.0942) = (6.57\%,9.43\%)[/tex]

(0.0657,0.0943)  is the 90% confidence interval for the population proportion of visitors that click on the advertisement.

Answer:

  f(x) = 2/(x -1) +1

Step-by-step explanation:

  [tex]f(x)=\dfrac{x+1}{x-1}=\dfrac{(x-1)+2}{x-1}=\dfrac{x-1}{x-1}+\dfrac{2}{x-1}\\\\\boxed{f(x)=\dfrac{2}{x-1}+1}[/tex]

Answer:

the second digit from the decimal, round it based on the the thousandth if above 5 round it to the next number 4 and below round it to the same number

Step-by-step explanation:

say for example 10.246 this would round to 10.25

another example is 10.244 this would round to 10.24

Answer:yes

Step-by-step explanation:

Answer:

[tex]x\geq \$40[/tex]

The graph in the attached figure

Step-by-step explanation:

Let

x ----> represents the amount that Jennifer has

y ----> represents the amount that Matthew has

we know that

The amount that Jennifer has is greater than or equal to $34 plus three times the samount that Matthew has

The inequality that represent this situation is

[tex]x\geq 3y+34[/tex]

we have

[tex]y=\$2[/tex]

substitute

[tex]x\geq 3(2)+34[/tex]

[tex]x\geq \$40[/tex]

The solution is the interval [40,∞)

In a number line the solution is the shaded area at right of x=40 (closed point)

see the graph attached

Inequality representing amount owed by Jennifer : x > 40

Important Information : Amount owed by Mathew =  $2

Amount owed by Jennifer = at least 34 more than triple amount owed by Mathew

So, x > 3 (2) + 34

x > 34 + 6

x > 40

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Answer:

Decreased by 60%

Step-by-step explanation:

First take the difference to the original amount to the new amount to find the change. 285 - 114 = 171

171/285 = .6

Multiply that by 100 to get it's percent.

The amount of shirts sold decreased by 60%

Final answer:

The percentage decrease in the average number of shirts sold in the shop from 285 to 114 shirts is 60%.

Explanation:

The percentage decrease in the average number of shirts sold at the beach shop can be calculated using the following formula: Percentage decrease = ((Original Average - New Average) / Original Average) × 100. The original average is 285 shirts, and the new average is 114 shirts after the temperature decrease.

So, the calculation would be: ((285 - 114) / 285) × 100 = (171 / 285) × 100 = 0.6 × 100 = 60%.

Therefore, the percentage decrease in the average number of shirts sold in the shop is 60%.

Answer:

= 10√3

Step-by-step explanation:

[tex]2 \sqrt{27} - \sqrt{48} + 4 \sqrt{12} \\ = (2 \times \sqrt{9 \times 3}) - (\sqrt{16 \times 3}) + (4 \times \sqrt{4 \times 3} )\\ = (2 \times 3 \sqrt{3}) - 4 \sqrt{3} + (4 \times 2 \sqrt{3} ) \\ = 6 \sqrt{3} - 4 \sqrt{3} + 8 \sqrt{3} \\ = 10 \sqrt{3} [/tex]

Answer:

10√3

Step-by-step explanation:

2√27 − √48 + 4√12

2√(3²×3) − √(4²×3) + 4√(2²×3)

6√3 − 4√3 + 8√3

√3(6 - 4 + 8)

10√3

There are 7,991 5-digit numbers that are divisible by either 45 or 60 but not divisible by 90.

To find the number of 5-digit numbers that are divisible by either 45 or 60 but not by 90, we can use the principle of inclusion-exclusion. First, let's find the number of 5-digit numbers divisible by 45 and the number divisible by 60, then subtract the number divisible by 90 to avoid overcounting.

A 5-digit number divisible by 45 must also be divisible by 9 and 5. The smallest 5-digit number divisible by 45 is 10005 (9 * 5 * 445), and the largest is 99990 (9 * 5 * 2222). We can find the number of 5-digit numbers divisible by 45 by subtracting the two numbers and adding 1 (99990 - 10005 + 1).

A 5-digit number divisible by 60 must also be divisible by 12 and 5. The smallest 5-digit number divisible by 60 is 10020 (12 * 5 * 167), and the largest is 99960 (12 * 5 * 833). We can find the number of 5-digit numbers divisible by 60 using the same method as before (99960 - 10020 + 1).

Finally, we subtract the number of 5-digit numbers divisible by 90. A 5-digit number divisible by 90 must be divisible by 45 and 2. The smallest 5-digit number divisible by 90 is 10035 (9 * 5 * 445 and 2 * 5017), and the largest is 99945 (9 * 5 * 2221 and 2 * 49973). Again, we use the same method as before to find the number of 5-digit numbers divisible by 90 (99945 - 10035 + 1).

To find the final answer, we subtract the number of 5-digit numbers divisible by 90 from the sum of the numbers divisible by 45 and 60.

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Answer:

No

Step-by-step explanation:

In different scenarios, the data will be different. However, sometimes, it's impossible to draw a histogram with equal widths, so in order to maintain clarity and fairness, the area of the bars should actually be proportional to the frequency, which is usually the y-axis of the graph or height of the bars.

Hope this helps!

Answer:

No

Step-by-step explanation:

Length is the frequency density which is obtained by:

Frequency/width

Height is not proportional to width.

Frequency is proportional to the area of the rectangle

Answer:

The null hypothesis was not rejected.  

The proportion of readers who own a personal computer is 47%.

Step-by-step explanation:

The claim made by a publisher is that 47% of  their readers own a personal computer.

A single proportion z-test can be used to determine whether the claim made by the publisher is authentic or not.

The hypothesis for this test can be defined as follows:

H₀: The proportion of readers who own a personal computer is 47%, i.e. p = 0.47.

Hₐ: The proportion of readers who own a personal computer is different from 47%, i.e. p ≠ 0.47.

The information provided is:

[tex]n=280\\\hat p=0.43\\\alpha =0.01[/tex]

The test statistic is:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.43-0.47}{\sqrt{\frac{0.47(1-0.47)}{280}}}=-1.34[/tex]

The test statistic value is, z = -1.34.

Decision rule:

If the p-value of the test is less than the significance level α = 0.01 then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

[tex]p-value=2\times P (Z < z)[/tex]

               [tex]=2\times P (Z < -1.34)\\=2\times [1-P(Z<1.34)]\\=2\times [1-0.90988]\\=0.18024\\\approx0.18[/tex]

*Use a z table for the probability.

The p-value of the test is 0.18.

p-value = 0.18 > α = 0.01

The null hypothesis was failed to be rejected at 1% level of significance.

Conclusion:

There is enough evidence to support the claim made by the publisher. Hence, it can be concluded that the proportion of readers who own a personal computer is 47%.

Answer:

Y=16928

Step-by-step explanation:

Answer:

Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out

Step-by-step explanation:

Answer:

I think that the answer is either A or C. I'm not too sure on which one.

Step-by-step explanation

Answer:

Probability that the test will lead the consumer group to "accept" the claimed mileage for this car is 0.00043.

Step-by-step explanation:

We are given that a consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level.

It is believed that the population standard deviation is 3 mpg. Based upon this information, the "true" population mean is 32.0 mpg.

Let [tex]\bar X[/tex] = sample mean highway miles per gallon

The z-score probability distribution for sample mean is given by;

                        Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = true population mean = 32.0 mpg

            [tex]\sigma[/tex] = population standard deviation = 3 mpg

            n = sample of cars = 100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that a mean highway miles per gallon of at least 33 actually meets this level is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 33)

  P([tex]\bar X[/tex] [tex]\geq[/tex] 33) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{33-32}{\frac{3}{\sqrt{100} } }[/tex] ) = P(Z [tex]\geq[/tex] 3.33) = 1 - P(Z < 3.33)

                                                = 1 - 0.99957 = 0.00043

The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.7673.

Therefore, the probability that the test will lead the consumer group to "accept" the claimed mileage for this car is 0.00043.

Answer:

−x2+3x−11

Step-by-step explanation:

−3x2+4x+2x2−x−11

(−3x2+2x2)+(4x−x)−11

−x2+3x−11

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

Step-by-step explanation:

See attached file for answer pls

The measure of each angle in the Summer Triangle depends on the position and alignment of the stars and cannot be determined without specific coordinates and time of observation.

The Summer Triangle is a prominent summer asterism formed by three bright stars: Vega, Deneb, and Altair. The measure of each angle in the Summer Triangle depends on the position and alignment of these stars in the sky. The angles cannot be determined without the specific coordinates and time of observation.

Astronomers use angles to measure the separation between celestial objects in the sky. A full circle has 360°, and the half-sphere of the sky from horizon to opposite horizon contains 180°. By measuring the angular separation between two stars or objects, astronomers can determine how far apart they appear in the sky. The angle is typically measured in degrees (°).

For example, if two stars are 18° apart, their separation spans about 1/10 of the dome of the sky. To give you a sense of how big a degree is, the full Moon is about half a degree across, which is similar to the width of your smallest finger (pinkie) seen at arm's length.

Given:

In ΔABC, AB = 5 unit, BC = 2 unit and ∠C = 90°

To find the The value of ∠B.

Formula

By Trigonometric Ratio we know,

[tex]cos \ \theta=\frac{adj}{hyp}[/tex]

Let us take ∠B = θ

With respect to θ, BC is the adjacent side and AB is the hypotenuse.

So,

[tex]cos \ \theta=\frac{BC}{AB}[/tex]

[tex]cos \ B=\frac{2}{5}[/tex]

     [tex]B=cos^{-1} (\frac{2}{5} )[/tex]

     [tex]B = 66.42^{\circ}[/tex]

Hence, the value of ∠B is 66.42°.

Answer:

High school students and their parents are often bombarded with SAT test prep applications as they get closer to the college application process. Exam preparation offers arrive in the mail; they are sent home by schools, and they are not cheap. (The Princeton Review "Ultimate Classroom" course costs $ 1,199 in New York City.) When students take these courses and do not see their scores improve, parents may wonder if their children have studied enough or if they have wasted their money.

Step-by-step explanation:

Previous year, the NACAC released a report concluding that exam preparation courses have minimal impact on improving SAT scores: approximately 10-20 points on average in math and 5-10 points on critical reading. The Association for college administration report also noted that this evidence is "contrary to claims made by many test preparation providers of large increases of 100 points or more on the SAT."

Kathleen Steinberg, a College Board spokeswoman, says that, on average, students who take the SAT twice only "increase their scores by about 30 points."

He further disclose that "The College Panel does not indorse taking the SAT more than twice, as there is no evidence to indicate that taking the test more than twice increases grade performance."

Parents might also be surprised at the actual average SAT scores: 501 in critical reading, 515 in math, and 493 in writing, according to Steinberg. (The highest score you can get in any section is 800).

Kaplan claimed that The Princeton Review's claims for score breaks were based on comparing the results of Princeton Review's "diagnostic" tests with the students' self-reported scores on the actual SAT tests, as opposed to SAT scores previous and after.

Final answer:

Test-preparation organizations like Kaplan, Princeton Review, etc. often claim that students gain an average of 100 or more points on the SAT after taking their classes. While it is possible for some students to achieve a significant score improvement after taking these classes, it is important to note that the average improvement may not be 100 points for every student.

Explanation:

Test-preparation organizations like Kaplan, Princeton Review, etc. often claim that students gain an average of 100 or more points on the SAT after taking their classes. While it is possible for some students to achieve a significant score improvement after taking these classes, it is important to note that the average improvement may not be 100 points for every student.

The effectiveness of these classes depends on various factors, such as the student's starting score, their commitment and effort in the class, and their ability to apply the strategies they learn. Some students may experience a smaller improvement, while others may see a larger gain.

It's recommended for students to research and read reviews before choosing a test-preparation organization to ensure they are selecting a reputable program that aligns with their learning style and goals.

Answer:

17x +21

Step-by-step explanation:

-3(x+3)+5(4x+6)

Distribute

-3x-9+20x+30

Combine like terms

17x +21