2y2(35 – 4y) in standard form

The anchor drops 63 meters in the first 5 seconds.

The given function E(t) = -2.4t + 75 represents the elevation of the ship's anchor relative to the water's surface at any given time t. To find how far the anchor drops every 5 seconds, substitute t = 5 into the function:

E(5) = -2.4(5) + 75

E(5) = -12 + 75

E(5) = 63

Therefore, after 5 seconds, the anchor has dropped 63 meters relative to the water's surface. This indicates the change in elevation during this time period. The negative coefficient of t in the function implies a downward motion, and the constant term (75) represents the initial height of the anchor above the water. So, the anchor drops 63 meters in the first 5 seconds.

Answer:

Correct option: (B) 71.89%.

Step-by-step explanation:

R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient of determination.

The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent variable).

The coefficient of determination R² can be computed by the formula,

[tex]R^{2}=\frac{SSR}{SST}[/tex]

Here,

SSR = sum of squares of regression

SST = sum of squares of total

From the output attached below the value of SSR and SST are:

SSR = 37043.3236

SST = 51531.0863

Compute the value of R² as follows:

[tex]R^{2}=\frac{SSR}{SST}[/tex]

     [tex]=\frac{37043.3236 }{51531.0863}[/tex]

     [tex]=0.7188539\\\approx 0.7189[/tex]

Thus, the fraction of the variability in house size is explained by income and size of family is 71.89%.

The correct option is (B).

To find the fraction of the variability in house size that is explained by family income and size, we sum the two SSR values and express this as a fraction or percentage of the total variability in house size. The actual value could not be determined from the provided information as it appears to be missing.

The question focuses on understanding the impact of family income and family size (the independent variables) on the house size (the dependent variable). The builder calculated the Sum of Squares for Regression (SSR) considering each independent variable given other independent variables constant. These calculations provide crucial insights into the contribution made by each independent variable to the variation in the dependent variable.

The total SSR (from both variables) can be calculated by summing the SSRs given: SSR(X1 ∣ X2) = 36400.6326 and SSR(X2 ∣ X1) = 3297.7917, which gives 39698.4243. This total variability is a representation of the entire variability in house size that is accounted for by both family income and family size. Express this as a fraction or percentage of total variability in house size to determine the proportion of variability explained by the two predictors.

Note: The Excel output and the options (A. 84.79%, B. 71.89%, C. 17.56%, D. 70.69%) should contain the exact proportion but in the provided information, these values are missing.

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Job A is the correct answer! :)

Based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.

The factors that should determine if a job should be accepted or not include:

                                          Job A          Job B            Job C

Salary                              $46,650     $38,750       $52,880

Benefits                             14,000        15,000           8,000

Average monthly rent          850             790               950

Annual rent                    $10,200       $9,480         $11,400 ($950 x 12)

Earnings before tax     $50,400     $44,270       $49,480

Thus, based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.

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Answer:The answer is 8x10^7

Step-by-step explanationi took the thing

Answer:

Chair is $1600

Table are 5 pieces

Step-by-step explanation:

Let the cost of a chair be x then for a table, it will be 5x since table cost 5 times as much as a chair.

For $40000, chairs alone will be 40000/x while tables will be 40000/5x=8000/x

The difference between these numbers is 20 hence

40000/x-8000/x=20

32000/x=20

X=32000/20=1600

The cost of a chair is $1600

Table will be 5*1600=$8000

The number bought will be proved as follows

Chairs=40000/1600=25 pieces

Tables=40000/8000=5 pieces

Difference in number is 25-5=20

Answer:

The probability that the sample mean would differ from the population mean by greater than 0.8 kg is P=0.3843.

Step-by-step explanation:

We have a population with mean 60 kg and a variance of 100 kg.

We take a sample of n=118 individuals and we want to calculate the probability that the sample mean will differ more than 0.8 from the population mean.

This can be calculated using the properties of the sampling distribution, and calculating the z-score taking into account the sample size.

The sampling distribution mean is equal to the population mean.

[tex]\mu_s=\mu=60[/tex]

The standard deviation of the sampling distribution is equal to:

[tex]\sigma_s=\sigma/\sqrt{n}=\sqrt{100}/\sqrt{118}=10/10.86=0.92[/tex]

We have to calculate the probability P(|Xs|>0.8). The z-scores for this can be calculated as:

[tex]z=(X-\mu_s)/\sigma_s=\pm0.8/0.92=\pm0.87[/tex]

Then, we have:

[tex]P(|X_s|>0.8)=P(|z|>0.87)=2*(P(z>0.87)=2*0.19215=0.3843[/tex]

Answer:

[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]

Step-by-step explanation:

[tex]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/tex]

[tex]cos(a+b)[/tex]

We need to expand cos(a+b) using the cos addition formula.

[tex]cos(a+b)=cos(a)cos(b)-sin(a)sin(b)[/tex]

We know that we also need to use Euler's formula for sin, which is:

[tex]sin(x)=\frac{e^{ix}-e^{-ix}}{2}[/tex] (you can get this from a similar way of getting the first result, of simply just expanding [tex]e^{ix}=cosx+isinx[/tex] and seeing the necessary result)

We can now substitute our cos's and sin's for e's

[tex]cos(a+b)=(\frac{e^{ia}+e^{-ia}}{2})(\frac{e^{ib}+e^{-ib}}{2})-(\frac{e^{ia}-e^{-ia}}{2})(\frac{e^{ib}-e^{-ib}}{2})[/tex]

Now lets multiply out both of our terms, I'm using the exponent multiplication identity here ([tex]e^{x+y}=e^xe^y[/tex])

[tex]cos(a+b)=\frac{e^{i(a+b)} + e^{i(a-b)}+e^{i(-a+b)} + e^{i(-a-b)}}{4}-\frac{e^{i(a+b)} - e^{i(a-b)}-e^{i(-a+b)}+e^{i(-a-b)}}{4}[/tex]

Now we can subtract these two terms.

[tex]cos(a+b)=\frac{2e^{i(a-b)}+2e^{i(-a+b)}}{4}[/tex]

This is starting to look a lot tidier, let's cancel the 2

[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]

Using Euler's formula, we can write cos(x) as the average of exp(ix) and exp(-ix). Further, we demonstrated how to express cos(a+b) and cos(a)cos(b) in terms of exponential functions, utilizing the properties of Euler's formula and complex exponentials.

Using Euler's formula, exp(ix) = cos(x) + i sin(x) and exp(-ix) = cos(x) - i sin(x), we can represent cos(x) as a combination of exp(ix) and exp(-ix). By adding these two equations, we eliminate the sin(x) terms due to their opposite signs, leading us to the formula for cos(x):

cos(x) = (exp(ix) + exp(-ix)) / 2

To express cos(a+b), use the expansion:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Using Euler's formula, this expands to:

cos(a+b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2 - [exp(ia) - exp(-ia)]/2i * [exp(ib) - exp(-ib)]/2i

Similarly, to express cos(a)cos(b), we again use the representation of cos(x) in terms of exp:

cos(a)cos(b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2

Answer: 144 square centimeters

Answer:

the answer is 144 centimeters

Answer:

8p^3(2p - 3) is the factor

Step-by-step explanation:

Answer:

100,000 lol

Step-by-step explanation:

Answer:

The numbers are 16 and 7

Step-by-step explanation:

Let the numbers be x and y

x+y = 23

x-y = 9

Add the two equations together

x+y = 23

x-y = 9

-------------------

2x = 32

Divide each side by 2

2x/2 = 32/2

x = 16

Now subtract the two equations

x+y = 23

-x +y = -9

-------------------

2y = 14

Divide by 2

2y/2 = 14/2

y = 7

Final answer:

The two numbers with a sum of 23 and a difference of 9 are 16 and 7. Solved by setting up equations for the sum and difference, then solving for the two unknowns.

Explanation:

To find the two numbers with a sum of 23 and a difference of 9, we can set up two equations based on the given information:

Adding the two equations together, we get:

2x = 32

Dividing both sides by 2:

x = 16

Now, substituting x back into one of the original equations, for example, x + y = 23:

16 + y = 23

y = 23 - 16

y = 7

Therefore, the two numbers are 16 and 7.

Answer:

Correct Answer: CA larger sample size results in a smaller margin error, i.e. with a plant of 100 plots instead of 25, the margin error will be smaller.

Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

An agricultural researcher plants 25 plots with a new variety of yellow corn.

Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean and standard deviation of 10.

We need to find a confidence interval with a smaller margin of error than the 90% confidence interval

n=25, x=150,s=10,a=0.95

Unknown mean u means we use t table.

[tex]150 ± t_{0.975} \frac{10}{\sqrt{25}}[/tex]

150±[tex]t_{0.975}[/tex]×2

Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error

Hence, option C is correct. Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error

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Answer:

Option B is not the most common correct choice.

Step-by-step explanation:

The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.

The probability that any of these five option is the correct answer is:

[tex]p=\frac{1}{5}=0.20[/tex]

A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.

The results showed that 90 of the 400 questions having B as the answer.

To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:

H₀: All the options are equally probable, i.e. p = 0.20.

Hₐ: Option B is more likely the correct option, i.e. p > 0.20.

Compute the sample proportion as follows:

[tex]\hat p=\frac{90}{400}=0.225[/tex]

The test statistic is:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.225-0.20}{\sqrt{\frac{0.20(1-0.20)}{400}}}= 1.25[/tex]

The test statistic is 1.25.

Decision rule:

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

Compute the p-value as follows:

[tex]p-value=P(Z>1.25)\\=1-P(Z<1.25)\\=1-0.89435\\=0.10565\\\approx 0.1057[/tex]

*Use a z-table.

The p-value is 0.1057.

The p-value of the test is quite large. Thus, the null hypothesis was failed to rejected.

Hence, it can be concluded that option B is not  the most common correct choice.

Testing the hypothesis, it is found that since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.

At the null hypothesis, it is tested if all of them are equally as likely, that is, the proportion of B is [tex]p = \frac{1}{5} = 0.2[/tex]. Thus:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if B is more likely, that is, if the proportion of B is more than 0.2. Thus:

[tex]H_1: p > 0.2[/tex]

The test statistic is given by:

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

In which:

In this problem, the parameters are: [tex]p = 0.2, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].

The value of the test statistic is:

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

[tex]z = \frac{0.225 - 0.2}{\sqrt{\frac{0.2(0.8)}{400}}}[/tex]

[tex]z = 1.25[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 1.25.

Looking at the z-table, z = 1.25 has a p-value of 0.8944.

1 - 0.8944 = 0.1056.

Since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.

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Answer:

2.68% probability that inflation will be above 13% next year

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 3.37, \sigma = 5[/tex]

If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year

This is the pvalue of Z when X = 13. So

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

[tex]Z = \frac{13 - 3.37}{5}[/tex]

[tex]Z = 1.93[/tex]

[tex]Z = 1.93[/tex] has a pvalue of 0.9732

1 - 0.9732 = 0.0268

2.68% probability that inflation will be above 13% next year

Answer:

[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]

And we can find this probability using the complement rule and the normal standard distirbution table or excel:

[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the annual inflation of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.37,5)[/tex]  

Where [tex]\mu=3.37[/tex] and [tex]\sigma=5[/tex]

We are interested on this probability

[tex]P(X>13)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]

And we can find this probability using the complement rule and the normal standard distirbution table or excel:

[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]

Answer:

(a)25 Milligrams

(b)15%

(c)[tex]A(10) = 25(0.85)^{10}[/tex]

Step-by-step explanation:

The amount in milligrams of a drug in the body t hours after taking a pill is given by the model:

[tex]A(t) = 25(0.85)^t[/tex]

(a)Comparing this with the exponential decay model, [tex]A(t)=A_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }[/tex], the initial dose given is 25 milligrams.

(b)From the model,

[tex]A(t) = 25(0.85)^t\\A(t) = 25(1-0.15)^t[/tex]

We can also use this method:

[tex]r = a - 1 = 0.85 - 1 = -0.15=-15\%[/tex]

We can see that for every hour, 15% of the drug leaves the body.

(c)After 10 hours

When t=10

[tex]A(10) = 25(0.85)^{10}[/tex]

The amount of drug left after 10 hours is given above in function notation.

a. The initial dose given is 25 milligrams. b. 85(0.85)^t percent of the drug leaves the body each hour. c. The amount of drug left after 10 hours is 0.2147 milligrams.

a. The initial dose given can be found by substituting t = 0 into the function A(t) = 25(0.85)^t. This gives A(0) = 25(0.85)^0 = 25(1) = 25 milligrams.

b. To find the percent of the drug that leaves the body each hour, we need to find the rate of change of A(t) with respect to time. Taking the derivative of A(t) gives dA/dt = 25(0.85)^t * ln(0.85) = 21.25(0.85)^t. This represents the rate of change of A(t) with respect to time. To find the percent, we can divide this rate by the initial dose and multiply by 100: (21.25(0.85)^t / 25) * 100 = 85(0.85)^t percent.

c. To find the amount of drug left after 10 hours, we substitute t = 10 into the function A(t) = 25(0.85)^t: A(10) = 25(0.85)^10 = 25(0.0859) = 0.2147 milligrams.

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Answer:

[tex] \epsilon = Y -X\beta[/tex]

And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:

[tex] Cov (\epsilon) = \sigma^2 I[/tex]

So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:

The regression model assumes the errors are normally distributed.

Step-by-step explanation:

Assuming that we have n observations from a dependent variable Y , given by [tex] Y_1, Y_2,....,Y_n[/tex]

And for each observation of Y we have an independent variable X, given by [tex] X_1, X_2,...,X_n[/tex]

We can write a linear model on this way:

[tex] Y = X \beta +\epsilon [/tex]

Where [tex]\epsilon_{nx1}[/tex] i a matrix for the error random variables, and for this case we can find the error ter like this:

[tex] \epsilon = Y -X\beta[/tex]

And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:

[tex] Cov (\epsilon) = \sigma^2 I[/tex]

So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:

The regression model assumes the errors are normally distributed.

Final answer:

The best statement is that the regression model assumes the errors are normally distributed. In regression analysis, it is essential that the errors are independent, normally distributed, and have constant variance, which supports the validity of the model's predictions.

Explanation:

The correct statement among the provided options is that the regression model assumes the errors are normally distributed. This is a fundamental assumption of linear regression analysis, where it's assumed that the residuals or errors of the regression model are randomly distributed about an average of zero. These error terms must be independent, normal, and have constant variance (homoscedasticity) across all levels of the independent variables.

According to the theoretical foundation of regression, it is not assumed that errors have an increasing mean, nor that they have zero variance, as some diversity in errors is expected. Additionally, the assumption that errors are indeed dependent would violate the principles of ordinary least squares (OLS) regression, making the model invalid.

Normality, independence, and equal variance are key premises in regression analysis to ensure the validity of the model's inferences. Indeterminate errors that affect the dependent variable 'y' are assumed to be normally distributed and independent of the independent variable 'x'. This maintains the integrity of the regression model.

Answer:

0.663

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 138.5, \sigma = 29[/tex]

What proportion of cars spends between 120 and 180 seconds in Wendy's drive-thru?

This is the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 120. So

X = 180

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

[tex]Z = \frac{180 - 138.5}{29}[/tex]

[tex]Z = 1.43[/tex]

[tex]Z = 1.43[/tex] has a pvalue of 0.924

X = 120

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

[tex]Z = \frac{120 - 138.5}{29}[/tex]

[tex]Z = -0.64[/tex]

[tex]Z = -0.64[/tex] has a pvalue of 0.261

0.924 - 0.261 = 0.663

Final answer:

0.662 when rounded to three decimal places.

Explanation:

To determine the proportion of cars that spend between 120 and 180 seconds in Wendy's drive-thru, we can use the properties of the normal distribution. Given that the mean time is 138.5 seconds and the standard deviation is 29 seconds, we can calculate the corresponding z-scores for both 120 seconds and 180 seconds.

Firstly, calculate the z-score for 120 seconds:
z = (X - µ) / σ = (120 - 138.5) / 29 ≈ -0.6379.

Next, calculate the z-score for 180 seconds:
z = (X - µ) / σ = (180 - 138.5) / 29 ≈ 1.4310.

By looking up these z-scores in a standard normal distribution table, we find that:
P(Z < 1.4310) ≈ 0.9236
P(Z < -0.6379) ≈ 0.2616.

To find the proportion of times between 120 and 180 seconds, we subtract the smaller probability from the larger:
P(120 < X < 180) = P(Z < 1.4310) - P(Z < -0.6379) ≈ 0.9236 - 0.2616 = 0.6620.

Answer:

a. The percentage of all taxpayers who file electronically is 58%

b. 654 people used an accountant or professional tax preparer preparing the tax return

Step-by-step explanation:

According to the given data, in order to estimate the percentage of all taxpayers who file electronically, we would have to make the following calculation:

percentage of all taxpayers who file electronically=634×100%=0.58

                                                                                    1,091

Hence, the percentage of all taxpayers who file electronically is 58%

In order to calculate how many people used an accountant or professional tax preparer for preparing the tax return, we would have to make the following calculation:

people used an accountant or professional tax preparer= 60%×1,091=654

                                                                                                 100%

654 people used an accountant or professional tax preparer preparing the tax return.

Answer:

[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]    

[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]    

So on this case the 98% confidence interval would be given by (3.767;4.233)

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=4[/tex] represent the sample mean

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

[tex]\sigma=1[/tex] represent the population standard deviation

n=100 represent the sample size  

Solution to the problem

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

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

Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that [tex]z_{\alpha/2}=2.326[/tex]

Now we have everything in order to replace into formula (1):

[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]    

[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]    

So on this case the 98% confidence interval would be given by (3.767;4.233)

Answer:

the answer is 13!

Step-by-step explanation:

hope this helps

Answer:

the answer is 13

Step-by-step explanation:

Answer:

The sample size condition for conducting a hypothesis test for a population proportion is satisfied for this question.

Step-by-step explanation:

a) The sample size condition for conducting a hypothesis test for a population proportion is satisfied is when

np > 5 and n(1 - p) > 5

n = sample size = 50

p = proportion that have STD = 18% = 0.18

np = 0.18 × 5 = 9 > 5

n(1 - p) = 0.82 × 50 = 41 > 5

Hope this Helps!!!

Answer:

Step-by-step explanation:

Given :

Answer:

8.8 ounces

Step-by-step explanation:

3.96/0.45=8.8

Answer: (ii) We reject H0---this sample provides significant evidence that the program is effective.

Step-by-step explanation:

The null hypothesis is

The program is not effective for weight loss.

The alternative hypothesis is

The program is effective for weight loss.

If the P-value for the test turns out to be 0.012, and the level of significance is 0.05, then

Alpha, 0.05 > p value, 0.012

Therefore, there is enough evidence to reject the null hypothesis. We then accept the alternative hypothesis.

The correct option is

(ii) We reject H0---this sample provides significant evidence that the program is effective.

Answer:

0.0515

Step-by-step explanation:

By the central limit theorem

when n increase distribution when data follows normal

Standard Error, SE of P is

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

Bootstrap Standard Error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

where n = 94 and p = 0.52

hence,

SE of Bootstrap = [tex]\sqrt{\frac{0.52(1-0.52)}{94} }[/tex]

[tex]=\sqrt{\frac{0.2496}{94} }\\\\=0.0515[/tex]

SE and the SE of Bootstrap are the same

Answer:

start at (0,0) and go up 1, right 1, and mark a point and keep doing that

Step-by-step explanation:

Answer:

255.75

Step-by-step explanation:

Answer:

$179.59

Step-by-step explanation:

Step 1 Write the exponential growth function for this situation.

y = a(1 + r)t Write the formula.

= 105(1 + 0.05)t Substitute 105 for a and 0.05 for r.

= 105(1.05)t Simplify.

Step 2 Find the value in 11 years.

y = 105(1.05)t Write the formula.

= 105(1.05)11 Substitute 11 for t.

≈ 179.59 Use a calculator and round to the nearest hundredth.

Answer:

Step-by-step explanation:

Type I error occurs when the null hypothesis is rejected even when it is true.

Type II error occurs when the null hypothesis is not rejected even when it is false.

The null hypothesis is

The mean annual consumption = the national mean

The alternative hypothesis is

The mean annual consumption < the national mean

1) it is a type II error because the null hypothesis was not rejected even when it is false

2) it is a correct decision because the decision corresponds to the outcome

3) it is also a type II error

d) it is a correct decision because the null hypothesis is accepted when it is true

By interpreting the various scenarios related to hypothesis testing, it is determined that scenarios 1 and 3 represent Type II errors, while scenarios 2 and 4 represent correct decisions. This shows an understanding of statistical hypothesis tests.

This problem falls within the discipline of statistical hypothesis testing, a method used to make statistical decisions using data. In the context of this problem, the null hypothesis states that the mean annual consumption of beer in the nation's capital is not less than the national mean.

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The solutions of the linear equation are; (2, 4), (3, 1) and (5, –5)

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The given linear equation is;

3x + y = 10

For (1, 6)

3x + y = 10

y = 10 - 3x

y = 10 - 3(1)

y = 10 -3 = 7

So, this is not the solution of the linear equation.

For (2, 4)

y = 10 - 3x

y = 10 - 3(2)

y = 10 -6 = 4

So, this is the solution of the linear equation.

For (3, 1)

y = 10 - 3x

y = 10 - 3(3)

y = 10 -9 = 1

So, this is the solution of the linear equation.

For (4, –1)

y = 10 - 3x

y = 10 - 3(4)

y = 10 -12 = -2

So, this is not the solution of the linear equation.

For (5, –5)

y = 10 - 3x

y = 10 - 3(5)

y = 10 -15 = -5

So, this is the solution of the linear equation.

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Answer:

B

Step-by-step explanation:

One-thirdx2y cm3 i got it right on edg

The volume of the pyramid with a square base of side x and height (y) is  (1/3)x²y cm³

Volume is the amount of space occupied by a three dimensional shape or object.

The area of the square base = x cm * x cm = x² cm²

The volume of the pyramid = (1/3) * area of square base * height = (1/3) * x² * y = (1/3)x²y cm³

The volume of the pyramid with a square base of side x and height (y) is  (1/3)x²y cm³

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