"The CEO of a large electric utility claims that 80% of all his customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73% say they are very satisfied. Were these surveyed customers less likely to be satisfied than all the CEO’s customers ( \alpha =0.05)?"

Correctly identifying shapes involves recognizing defining features. Figures A, C, and E are accurately labeled, while B and D need correction due to misclassifications.

In mathematics, shapes are defined by their boundaries or contours, often enclosed by points, lines, curves, and more. These characteristics categorize shapes into various types. The identification of shapes involves recognizing their defining features.

Analyzing the provided shapes:

Figure A is correctly identified as a cylinder. Its appearance aligns with the characteristics of a cylinder.

Figure B is mistakenly labeled as a square pyramid when, in fact, it resembles a cone. This discrepancy points to an incorrect classification.

Figure C is accurately described as having no bases, resembling a sphere. The absence of a base is a defining feature of a sphere.

Figure D is erroneously labeled as a triangular prism, whereas it more closely resembles a rectangular prism. This misclassification may lead to confusion.

Additionally, Figure D is correctly recognized for having four lateral faces that are triangles, aligning with the characteristics of a rectangular prism.

In summary, the accurate identifications are A, C, and E, while B and D require correction based on their actual geometric features.

Answer:

Step-by-step explanation:

An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money?

To solve this problem, we will simply write 1,00,000 in base 2.

2^17 gives 131072, 2^16 gives 65536.

So, the first gift is 65536, we then need to repeat this process for  34,464 ((100,000-65536 = 34,464), to get all gifts in succession.

6 gifts in all: one each of $32, $128, $512, $1024, $32768, and $65536.

Answer:

Step-by-step explanation:

Given the equation of the hyperbola

[tex]\dfrac{(x+2)^2}{144}-\dfrac{(y-4)^2}{81} =1[/tex]

Since the x part is added, then

[tex]a^2=144; b^2=81\\a=12,b=9[/tex]

Also, this hyperbola's foci and vertices are to the left and right of the center, on a horizontal line paralleling the x-axis.

From the equation, clearly the center is at (h, k) = (–2, 4). Since the vertices are a = 12 units to either side, then they are at (-14,4) and (10,4).

From the equation

[tex]c^2=a^2+b^2=144+81=225\\c=15[/tex]

The foci, being 15 units to either side of the center, must be at (–17, 4) and (13, 4)

Answer:log3 + log8

Step-by-step explanation:

log(3x8)=log3 + log8

The appropriate null and alternative hypotheses for the consumer watch group's hypothesis test on the hypnosis program's success rate are:

option a) H0: p = 0.57 vs. Ha: p < 0.57

The Null Hypothesis (H0):The success rate of the hypnosis program is 57%.

Alternative Hypothesis (Ha): The success rate is less than 57%.

We use a one-tailed test because we have a directional hypothesis (suspecting a lower success rate).

If we suspected a higher or different rate, we'd use a two-tailed test.

The consumer watch group is challenging the claim of a 57% success rate by testing if the actual success rate is lower than 57%. This setup allows for a focused investigation into the program's effectiveness.

The complete question is :A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?

a) H0: p = 0.57 vs. Ha: p < 0.57

b) H0: p = 0.57 vs. Ha: p > 0.57

c) H0: p = 0.57 vs. Ha: p ≠ 0.57

d) H0: p < 0.57 vs. Ha: p > 0.57

Answer:

The sample proportion of successful procedures is 0.962.

Step-by-step explanation:

The sample proportion of successful procedures is the number of successfiç procedures divided by the total number of procedures.

In this problem:

158 procedures, of which 152 were successful. So

p = 152/158 = 0.962

The sample proportion of successful procedures is 0.962.

The sample proportion is the ratio of the number of successes to the total number of samples or trials, Hence, the sample proportion is 0.962

Given the Parameters :

The sample proportion can be calculated using the relation :

Sample proportion = 152/158 = 0.962

Hence, the sampling proportion of successful procedures is 0.962.

Learn more : https://brainly.com/question/18651667

Answer:

78.52% probability that the sample mean is greater than 320 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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 [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

In this problem, we have that:

[tex]\mu = 330, \sigma = 80, n = 40, s = \frac{80}{\sqrt{40}} = 12.65[/tex]

What is the likelihood the sample mean is greater than 320 minutes?

This is 1 subtracted by the pvalue of Z when X = 320. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{320 - 330}{12.65}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a pvalue of 0.2148

1 - 0.2148 = 0.7852

78.52% probability that the sample mean is greater than 320 minutes

Answer:

a) Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.

b) 69.51% of those who ran the marathon has a finishing time less than 272.

c) The spread in the distribution of women's finishing time is greater as compared to the spread in the distribution of men's finishing time.

Step-by-step explanation:

Part a) It was given that, the finishing time for Clay's marathon time is 289 minutes.

To calculate the standardized test score for Clay's marathon time, we use the formula:

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

where

[tex]x = 289[/tex]

[tex] \mu = 242[/tex]

and

[tex] \sigma = 29[/tex]

We substitute the values into the formula to get:

[tex]z = \frac{289 - 242}{29} = 1.62[/tex]

Interpretation: Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.

b) To calculate the proportion of women that had a finishing time less than Kathy , we again need to calculate the z-score for x=272, with mean for women being 259 minutes and standard deviation 32 minutes.

We substitute to get:

[tex]z = \frac{272 - 259}{32} = 0.41[/tex]

From the standard normal distribution table, P(z<0.41)=0.6951

Therefore 69.51% of those who ran the marathon has a finishing time less than 272.

c) The standard deviation measures the variation of a distribution. This means the standard deviation measures how far away the data set of a distribution are from the mean.

If the standard deviation of finishing time is greater for women than for men, then it indicates that, women's finishing time are far away from the mean finishing time as compared to men's finishing time.

Answer:

53

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

[tex](14 - 8) \ast8 + 5 \\ =6 \ast8 + 5 \\ = 48 + 5 \\ = 53 \\ \\ \red{ \boxed{\bold {\therefore \: (14 - 8) \ast8 + 5 = 53}}}[/tex]

Answer:

Step-by-step explanation:

Confidence interval for the difference in the two proportions is written as

Difference in sample proportions ± margin of error

Sample proportion, p= x/n

Where x = number of success

n = number of samples

For the men,

x = 318

n1 = 520

p1 = 318/520 = 0.61

For the women

x = 379

n2 = 460

p2 = 379/460 = 0.82

Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Margin of error = 1.96 × √[0.61(1 - 0.61)/520 + 0.82(1 - 0.82)/460]

= 1.96 × √0.0004575 + 0.00032086957)

= 0.055

Confidence interval = 0.61 - 0.82 ± 0.055

= - 0.21 ± 0.055

Answer:

y= 3x+4

Step-by-step explanation:

standard form is always y equals first

Answer: 21.3 miles

Step-by-step explanation:

Answer:

[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]  

[tex]p_v =P(z>0.6)=0.274[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

X=53 represent the people who prefer Pepsi

[tex]\hat p=\frac{53}{100}=0.53[/tex] estimated proportion of people who prefer PEsi

[tex]p_o=0.5[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5.:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>0.6)=0.274[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%

To determine if more than 50% of people prefer Pepsi to Coca-Cola, conduct a one-sample proportion test using the given data and a significance level of 0.05.

To conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to Coca-Cola, you can use a one-sample proportion test. The null hypothesis, denoted as H0, is that the proportion of people who prefer Pepsi is equal to 50%. The alternative hypothesis, denoted as H1, is that the proportion is greater than 50%. Using the given data, you would calculate the test statistic and compare it to the critical value or p-value associated with a significance level of 0.05. If the test statistic falls in the rejection region, you would reject the null hypothesis and conclude that more than 50% of people prefer Pepsi.

https://brainly.com/question/34171008

#SPJ3

Answer:

B. 0.3 and 0.022

Step-by-step explanation:

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 [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

For a sample proportion p in a sample of size n, the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

135 of the 450 residents sampled live within one mile of a hazardous waste site.

So the sample proportion is [tex]p = \frac{135}{450} = 0.3[/tex]

Standard error

[tex]s = \sqrt{\frac{0.3*0.7}{450}} = 0.022[/tex]

So the correct answer is:

B. 0.3 and 0.022

Final answer:

The sample proportion of people who live within one mile of a hazardous waste site is 0.3, and the standard error for this sample proportion is 0.022. The correct answer is B. 0.3 and 0.022.

Explanation:

To estimate the proportion of people who live within one mile of a hazardous waste site using a sample, we divide the number of residents living within one mile by the total number of residents sampled. In this case, 135 residents live within one mile out of a sample of 450 residents, which makes the sample proportion 135/450 = 0.3.

To calculate the standard error (SE) for the sample proportion, we use the formula SE = √(p(1-p)/n), where p is the sample proportion and n is the sample size. Plugging in the values, we get SE = √(0.3(1-0.3)/450), which approximates to 0.022.

The correct answer is B. 0.3 and 0.022 for the sample proportion and its standard error, respectively.

Answer:

Step-by-step explanation:

You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...

  sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)

  -sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)

Of course, you know that ...

  sin(π/4) = cos(π/4) = (√2)/2

  cos(π/3) = 1/2

  sin(π/3) = (√3)/2

So, the desired value is ...

  sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)

Comparing this form to the desired answer form, we see ...

  A = 2

  B = 3

Answer:

x = 16°, tan x = 0.3

Step-by-step explanation:

[tex]sin \: 2x = cos \: (3x + 10) \\ cos(90 - 2x) = cos \: (3x + 10) \\ 90 - 2x = 3x + 10 \\ 90 - 10 = 3x + 2x \\ 80 = 5x \\ x = \frac{80}{5} \\ \huge \red{ \boxed{x = 16 \degree }}\\ \\ tan \: x = tan \: 16 \degree \\ = 0.2867453858 \\ = 0.3[/tex]

Answer:

Yes,it is

Step-by-step explanation:

95's square root is 9.7467943448

10 is greater than 9.7 and so forth.

So the square root of 95 is less than 10.

The square root of 95 is approximately 9.74679434, thus the square root of 95 is less than 10. The question pertains to the mathematical operation of finding square roots that are indeed pivotal while solving various mathematical problems.

The student question asks if the square root of 95 is less than 10. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 95 is approximately 9.74679434, which is indeed less than 10. The concept of square roots comes from the realm of Mathematics, more specifically Algebra. It's crucial to understand this mathematical operation as it is frequently encountered in various mathematical problems, especially ones involving quadratic equations where an unknown variable is squared. Usually, these equations will yield two solutions, as both a positive and a negative number squared gives the same result. However, the context of a problem can sometimes restrict the solution to only one value, typically the positive.

As an example, let's consider an equation like x² = 49. The solutions to this are x = -7 and x = 7 because both (-7)² and 7² equals 49. But if this equation was describing a real-world scenario where negative values could not apply (like time or distance), the meaningful solution would only be x = 7.

For more about Square Root:

https://brainly.com/question/1540542

#SPJ3

Answer:4

Step-by-step explanation:

Complete Question:

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 1 2, 201 2). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries

Answer:

Null hypothesis, H₀ : μ = 24.57

Alternative hypothesis, [tex]H_{a}[/tex] :  μ ≠ 24.57

Step-by-step explanation:

The mean hourly wage for the goods producing industry = $24.57

Since we want to see  if the mean of hourly wage for the manufacturing industry is equal to $24.57( The mean f hourly wage for the good producing industry)

Therefore the, null hypothesis will be that there is no significant difference between the means of the hourly wages of both the goods producing and the manufacturing industries, while the alternative hypothesis will be that the means of their hourly wages are significantly different

Null hypothesis, H₀ : μ = 24.57

Alternative hypothesis, [tex]H_{a}[/tex] :  μ ≠ 24.57

Answer:

[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]

[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]

The 85% confidence interval would be given by (0.696;0.744)

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".  

Solution to the problem

The estimated proportion for this case is [tex]\hat p =\frac{700}{972}=0.720[/tex]

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 85% of confidence, our significance level would be given by [tex]\alpha=1-0.85=0.15[/tex] and [tex]\alpha/2 =0.075[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.44, z_{1-\alpha/2}=1.44[/tex]

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

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values obtained we got:

[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]

[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]

The 85% confidence interval would be given by (0.696;0.744)

We can set up a proportion since we know the ratio between the # of purple marbles and the # of green marbles.

A ratio is a way to compare two different values: for every 8 purple marbles there are 5 green marbles

The response variable in this model is:  Market value .

Hence the correct option is C.

Given, that a regression model is developed.

A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is market value .

Therefore the correct option is C .

Know more about regression model,

https://brainly.com/question/33168340

#SPJ4

In the regression model being developed by the real estate appraiser, the response variable is the market value of the single-family residential houses.

In the regression model described by the question, the market value of single-family residential houses is being predicted based on several predictive variables (heated area, number of bedrooms, number of bathrooms, age of the house, and presence of central heating). Therefore, the response variable or the dependent variable in this model is the market value of the houses.

A response variable is the feature or quantity that the model outputs. In this context, the real estate appraiser is trying to produce a model that will tell him how changes in the variables like heated area, bedrooms etc. will change the output, which is the market value.

https://brainly.com/question/32621004

#SPJ3  

Answer:

OptionB

Step-by-step explanation:

Answer:

0.826%

Step-by-step explanation:

The Rydberg constant = 2.178 × [tex]10^{-18}[/tex] J.

students record = 2.16 x [tex]10^{-18}[/tex]J.

error = 0.018 x [tex]10^{-18}[/tex]J.

Percentage error = [tex]\frac{error}{actual measurement}[/tex] x 100

  = [tex]\frac{ 0.018 * 10^{-18} }{2.178 * 10^{-18} }[/tex] x 100

  = 0.826%

Answer:

$4.80

Step-by-step explanation:

Make a proportion

$12 for 2.5 pounds, and $x for 1 pound

12/2.5=x/1

x/1 is equivalent to x

12/2.5=x

Divide

x=4.8

So, one pound of peanuts costs $4.80

Answer:

4.8

Step-by-step explanation:

divide 12.00 by 2.5 to find the unit rate which is 4.8.

The equation of motion for the given scenario, involving a 1-slug mass attached to a spring, an applied external force and a damping force, is determined by formulating a differential equation from Newton's 2nd law, incorporating the spring's force and the damping force. (a) The final equation is: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t).

The given scenario relates to the field of physics, specifically harmonic motion and dampening force. Harmonic motion can be studied in the context of a mass attached to a spring, such as in this question. Here, it's specified that we have a 1-slug mass attached to a spring with a spring constant of 5lb/ft, and that an external force, f(t) = 16 cos 2t + 4 sin 2t, is applied.

To find the equation of motion, you can use the general formula from Newton's 2nd law, F=ma. Given that the movement takes place in a medium providing a damping force numerically equal to two times the instantaneous velocity, the force equation of the damped harmonic oscillator becomes relevant.

The damping force can be represented as - 2v and the spring force represented as - 5x (as F= -kx). Hence, the differential equation F=ma can be represented as: m* d²x/ dt² = -2v * dx/dt – 5x + f(t), translating to: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t). This equation represents the equation of motion for the given conditions.

https://brainly.com/question/35885185

#SPJ3

Answer:

Triangle

Step-by-step explanation:

I got done taking the quiz and it wasn't oval For k12 people this is the answer. Hope this helps

Answer: [tex]x=9[/tex]

Divide both side by 5

[tex]5x/5=45/5\\x=9[/tex]

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

[tex]5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]

hope this helps you.....

Answer:

The height of the tower is 245 m

Step-by-step explanation:

The complete question in English is

Find the height of the tower with the data provided by the engineering team. Value of the segment ab= 50 m. The length between the child and the tip of the tower is 250 m

The picture in the attached figure

we know that

In the right triangle ABC

Applying the Pythagorean Theorem

[tex]AC^2=AB^2+BC^2[/tex]

we have

[tex]AB=50\ m\\AC=250\ m[/tex]

substitute

[tex]250^2=50^2+BC^2[/tex]

[tex]BC^2=250^2-50^2[/tex]

[tex]BC^2=60,000\\BC=245\ m[/tex]

Answer:

a)We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:  

Null hypothesis:[tex]p \leq 0.04[/tex]  

Alternative hypothesis:[tex]p > 0.04[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

b) We need to use a z statistic

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>8.396) \approx 0[/tex]  

Step-by-step explanation:

Data given and notation

n=400 represent the random sample taken

X=54 represent the number of failures

[tex]\hat p=\frac{54}{400}=0.135[/tex] estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

[tex]p_o=0.04[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:  

Null hypothesis:[tex]p \leq 0.04[/tex]  

Alternative hypothesis:[tex]p > 0.04[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Part b: Calculate the statistic  

We need to use a z statistic

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>8.396) \approx 0[/tex]  

So the p value obtained was a very low value and using the significance level for example [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives is significantly higher than 0.04 or 4%