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ad-work [718]
3 years ago
11

A random sample of 38 wheel chair users were asked whether they preferred cushion type A or B, and 28 of them preferred type A w

hereas only 10 of them preferred type B. Use a hypothesis test to assess whether it is fair to conclude that cushion type A is at least twice as popular as cushion type B.
Mathematics
1 answer:
-BARSIC- [3]3 years ago
7 0

Answer:

The statement that cushion A is twice as popular as cushion B cannot be verified

Step-by-step explanation:

From the question we are told that:

Sample size n=38

Type a size A X_a=28

Type a size B X_b=10  

Generally the probability of choosing cushion A P(a) is mathematically given by

P(a)=\frac{28}{38}

P(a)=0.73

Generally the equation for A to be twice as popular as B is mathematically given by

P(b)+2P(b)=3P

Therefore Hypothesis

Null H_0: p \leq \frac{2P}{3P} \\Altenative H_A:p>\frac{2P}{3P}

Generally the equation normal approx of p value is mathematically given by

z=\frac{x-np_0-0.5}{\sqrt{np_0(1-p_0)} }

z=\frac{28-(38*2/3)_0-0.5}{\sqrt{38*2/3*1/3} }

z=0.75

Therefore from distribution table

Pvalue=1-\theta (0.75)

Pvalue=0.227

Therefore there is no sufficient evidence to disagree with  the Null hypothesis H_0

Therefore the statement that cushion A is twice as popular as cushion B cannot be verified

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Body armor provides critical protection for law enforcement personnel, but it does affect balance and mobility. The article "Imp
yKpoI14uk [10]

Answer:

No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that true average task time with armor is less than 2 seconds.

Then, the null and alternative hypothesis are:

H_0: \mu=2\\\\H_a:\mu< 2

The significance level is 0.01.

The sample has a size n=52.

The sample mean is M=1.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.2}{\sqrt{52}}=0.028

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1.95-2}{0.028}=\dfrac{-0.05}{0.028}=-1.803

The degrees of freedom for this sample size are:

df=n-1=52-1=51

This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

3 0
3 years ago
A. x+x+x+3x+3x=9<br> B. x+x+x+x+x=18<br> C. x+x+x+3x+3x=18<br> D. 9x^5=18
lisov135 [29]

9514 1404 393

Answer:

  a)  C  x +x +x +3x +3x = 18

  b)  x = 2

  c)  2 cm, 6 cm

Step-by-step explanation:

a) The sum of the lengths of the sides is equal to the length of the perimeter. The appropriate equation is ...

 x +x +x +3x +3x = 18

__

b) Simplifying, the equation becomes ...

  9x = 18

  x = 2 . . . . . divide by 9

__

c) The shorter sides are x = 2 cm.

The longer sides are 3x = 6 cm.

6 0
3 years ago
An angle measures 34 degrees more than the measure of its complementary angle what is the measure of each angle
adelina 88 [10]
Given that x is 34° more than its complement y. Hence, measure of the supposed angle is 107°.
7 0
2 years ago
How do I find 60% of £500?
MA_775_DIABLO [31]

Answer: 300

Step-by-step explanation:

60% = 60/100

500 x 60/100 = 300

8 0
3 years ago
Read 2 more answers
Assume that all triangles have interior angles less than 90°.A surveyor sights on a survey marker that is 132.3m distant. She ne
Vadim26 [7]

Answer:

  85.9 m

Step-by-step explanation:

The law of sines can help figure this.

The remaining angle in the triangle is ...

  180° -75° -68° = 37°

This is the angle opposite the leg from the surveyor to the second marker. Referencing the attachment, we have ...

  b/sin(B) = c/sin(C)

  b = sin(B)·c/sin(C) = 132.3·sin(37°)/sin(68°) ≈ 85.873 . . . meters

The surveyor is about 85.9 meters from the second marker.

4 0
3 years ago
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