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tamaranim1 [39]

3 years ago

7

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Y

our sample size is 4. Find the critical value that corresponds to a confidence level of 98%. (Report answer accurate to three decimal places with appropriate rounding.)

1 answer:

Luda [366]3 years ago

6 0

Answer:

T = 4.541

Step-by-step explanation:

We don't have the standard deviation for the population, so we use the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 4 - 1 = 3

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 4.541

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The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since

ikadub [295]

Answer:

a) "This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b) "They will decide the stands are safe when they're not."

c) "They will decide the stands are unsafe when they are in fact safe."

Step-by-step explanation:

a) As the alternative hypothesis Ha is μ>575, the rejection region lays in the upper tail. Then, it is an upper-tail test.

They are testing the claim that the stand supports an average of 575 pounds or more, and are looking for statistical evidence for that claim.

"This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b) A Type I error happens when a true null hypothesis is rejected.

This would mean that a stands that doesn't really hold 575 pounds or more has passed the test. The stand would appear more safe than it is.

"They will decide the stands are safe when they're not."

c) A Type II error happens when a false null hypothesis failed to be rejected. In this case, a safe stand, that suports 575 pounds or more, does not pass the test.

"They will decide the stands are unsafe when they are in fact safe."

4 0

3 years ago

Train X traveled 216.6 kilometers in 38 minutes. How many miles per hour was it traveling?

lara31 [8.8K]

Answer:

210 miles in 1 hour

Step-by-step explanation:

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6 0

3 years ago

4 divided by 5 minus radical 15

forsale [732]

-3.073 that is the correct answer

3 0

3 years ago

Evaluate the quotient of 1.05 x 103 and 1 x 103:

Mama L [17]

1.5 * 103= 108.15
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8 0

3 years ago

Read 2 more answers

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

$f(x)=3x(x^2-5x+x-5)$

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0

3 years ago