I need help quick 16 mins left and I’m on the last question

Someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi. We think the

denpristay [2]

Answer:

The sample size must be greater than 37 if we want to reject the null hypothesis.

Step-by-step explanation:

We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.

Also, we are given a level of significance of 5%.

Let $\mu$ = <u><em>mean breaking strength of their climbing rope</em></u>

SO, Null Hypothesis, $H_0$ : $\mu$ = 2,000 psi {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, $H_A$ : $\mu$ < 2,000 psi {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = ample mean strength = 1,997.2956 psi

$\sigma$ = population standard devaition = 10 psi

n = sample size

Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

SO, T.S. < -1.645 {then reject null hypothesis}

$\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645$

$\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645$

$(\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645$

$-0.27044 \times \sqrt{n}< -1.645$

$\sqrt{n}> \frac{-1.645}{-0.27044}$

$\sqrt{n}>6.083$

n > 36.99 ≈ 37.

SO, the sample size must be greater than 37 if we want to reject the null hypothesis.

7 0

4 years ago

Darlene is building a rectangular fence. the length is 8 feet longer than the width. the perimeter of the rectangle is 76 feet.

Llana [10]

Answer:8 feet

Step-by-step explanation:

4 0

2 years ago

Which expression is equivalent to sin(2x) cosx

Vsevolod [243]

Answer:

$2sin(x)cos^2(x)$

Step-by-step explanation:

To solve the problem, you must expand the trigonometric expression using the information given.

$sin(2x)cosx\\sin(2x)\\=2sin(x)\\=2sin(x)cos^2(x)$

7 0

2 years ago

Each person in a large square occupies, on average, 2.5 sq. feet of space. Estimate the number of people that can comfortably st

Aleksandr [31]

Answer:

2000 people

Step-by-step explanation:

The area of the gym is the width times length:

A = wl

A = (50 ft) (100 ft)

A = 5000 ft²

Write a proportion:

1 person / 2.5 ft² = x / 5000 ft²

x = 2000 people

3 0

3 years ago

Read 2 more answers

Can you guys help me with this please it suppose to use the synthetic substitution or the remainder theorem.

Brilliant_brown [7]

9514 1404 393

Answer:

(b) -36

Step-by-step explanation:

Synthetic division is often performed using a table of the kind shown in the attachment. The coefficients of f(x) are placed across the top, and the x-value to be evaluated is placed at the left. The rule for finding table entries is shown. (The first (left-most) number at the bottom is the leading coefficient of the polynomial.)

This table shows the remainder, which is f(-2), is -36.

__

The equation itself can be rewritten in "Horner form" to facilitate evaluation.

f(x) = (((-x +2)x -1)x +4)x +8

In this form, substituting for x and doing the evaluation is easier for mental arithmetic. You will notice that the contents of parentheses at each level match the bottom line of the synthetic division table.

f(-2) = (((-(-2) +2)(-2) -1)(-2) +4)(-2) +8

= (((4)(-2) -1)(-2) +4)(-2) +8

= ((-9)(-2) +4)(-2) +8

= (22)(-2) +8

= -36

f(-2) = -36 . . . . remainder from synthetic substitution

6 0

3 years ago