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The US Census reported that it takes workers an average of 28 minutes to get home from work with standard deviation 5 minutes. A

xz_007 [3.2K]

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

$H_0: \mu = 28$

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

$H_1: \mu > 28$ .

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the sample.

n is the sample size.

In this problem, the values of the parameters are given by:

$\overline{x} = 32, \mu = 28, \sigma = 5, n = 10$

Hence:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}$

$z = 2.53$

<h3>What is the decision?</h3>

Considering that we have a <em>right-tailed test</em>, as we are testing if the mean is greater than a value, with a standard <em>significance level of 0.05</em>, the critical value is of $z^\ast = 1.645$ .

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

To learn more about the z-distribution, you can check brainly.com/question/26454209

4 0

2 years ago

And this figure 14.2% of the area is painted green. how much of the area is paint a great?

Anna11 [10]

Answer:

Answer: . Area of figure = area of squane + anea

of tringle =side * side + 1/2 xbagex height =7 * 7+

1/2 * 7 *

8 0

2 years ago

Read 2 more answers

Hi! i’ll mark brainlest to whoever answers this question first :(

earnstyle [38]

Answer:

-5,5

Step-by-step explanation:

8 0

3 years ago

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2/5(g - 7) = 3 <br> can i please get some help..

Flura [38]

Answer:

14.500

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(2)/(5)*(g-7)-(3)=0

Step by step solution :

STEP

1

:

2

Simplify —

5

Equation at the end of step

1

:

2

(— • (g - 7)) - 3 = 0

5

STEP

2

:

Equation at the end of step 2

2 • (g - 7)

——————————— - 3 = 0

5

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 5 as the denominator :

3 3 • 5

3 = — = —————

1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 • (g-7) - (3 • 5) 2g - 29

——————————————————— = ———————

5 5

Equation at the end of step

3

:

2g - 29

——————— = 0

5

STEP

4

:

When a fraction equals zero

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

2g-29

————— • 5 = 0 • 5

5

Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2g-29 = 0

Solving a Single Variable Equation:

4.2 Solve : 2g-29 = 0

Add 29 to both sides of the equation :

2g = 29

Divide both sides of the equation by 2:

g = 29/2 = 14.500

One solution was found :

g = 29/2 = 14.500

8 0

3 years ago

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Neela is making rectangular place mats that are 12 inches wide and 15 inches long. What is the least amount of ribbon that she w

schepotkina [342]

Believe it or not, :), the width of the ribbon needs to be known to get the right answer. If the ribbon had an infinitely small width the ribbon needed would just be the perimeter.

P=2(L+W)

P=2(12+15)

P=54 in

However an infinitely small width is not something that has any practical application. For example, if the width of the ribbon were 1/2 in.

P=2((L+1)+W)

P=2(16+12)

P=56 in So the perimeter increased by 2 in when the ribbon was only 1/2 in wide.

The "infinitely small" width and the perimeter of 54 in is only a decent approximation if the ribbon were a very thin string.

8 0

4 years ago