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9 days ago

In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK? Point G cannot be a ce

ntroid because JG does not equal GE. Point G cannot be a centroid because JG is shorter than GE. Point G can be a centroid because GE and JG are in the ratio 2:1. Point G can be a centroid because JG + GE = JE.

Mathematics

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Question 1 Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your metho

babunello [11817]

Answer:

(a) The 95% confidence interval representing the percentage of the entire U.S. population that would select American football as their preferred television sport is (0.34, 0.40).

(b) Not reasonable.

Step-by-step explanation:

Given:

n = 1000

$\hat p$ = 0.37

(a)

The confidence interval (1 - α)% for proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Where:

$\hat p$ = the sample proportion

n = sample size

$z_{\alpha/2}$ = critical z value.

Calculate the critical value of z for a 95% confidence level as shown:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Refer to a z-table for the necessary value.

Compute the 95% confidence interval for proportion p as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.37\pm 1.96\times\sqrt{\frac{0.37(1-0.37)}{1000}}$

$=0.37\pm 0.03\\=(0.34, 0.40)$

Thus, the 95% confidence interval indicating the proportion of individuals in the U.S. who might say their preferred sport on TV is American football is (0.34, 0.40).

(b)

Next, we must assess if it's rational to consider that the actual percent of people in the United States who favor American football on television is 33%.

The hypothesis is defined as:

H₀: The portion of the U.S. population claiming American football as their favorite sport on television is 33%, meaning p = 0.33.

Hₐ: The proportion of people in the U.S. whose favorite sport to watch on television is not 33%, or p ≠ 0.33

This hypothesis can be verified using a confidence interval.

The decision rule:

If the (1 - α)% confidence interval contains the null value of the hypothesis, then the null hypothesis is not rejected. If, however, the (1 - α)% confidence interval excludes the null value of the hypothesis, then the null hypothesis is rejected.

The confidence interval does encompass the null value of p, which is 0.33.

<pthus the="" null="" hypothesis="" will="" be="" rejected.=""><pin conclusion="" it="" is="">not reasonable to accept that 33% represents the actual percentage of those in the U.S. whose favorite televised sport is American football.

</pin></pthus></pthe>

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3 months ago

Men absolute deviation of 14, 8, 7,6,5,10,11,8,8,6

Inessa [12570]

I am not very familiar with this topic, but it seems to me that the average is around 8, which would suggest a deviation of approximately 2.

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2 months ago

The two circles shown above have radii of 8 in. and 4 in. What is the Circumference of the both?

lawyer [12517]

The Circumference of Circle 1 measures 50.24 inches, while Circle 2 measures 25.12 inches. For calculations, Circle 1 has a radius of 8 inches and Circle 2 a radius of 4 inches. To compute circumferences, we utilize the formula for calculating circumference involving the value of π. Substituting the respective radius values into the formula produces the computed circumferences.

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2 months ago

Let a⃗ =4ı^−2ȷ^, b⃗ =−3ı^+5ȷ^, and e⃗ =2a⃗ +3b⃗ . part a write vector e⃗ in component form.

zzz [12365]

We are provided with the vectors:

Vector $\vec{a}=4\hat i-2\hat j$ and $\vec{b}=-3\hat i+5\hat j$ .