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S_A_V [24]
3 years ago
12

The mean salary of people living in a certain city is $37500 with a standard deviation of $1561. a sample of 33 people is select

ed at random from those living in the city. find the probability that the mean income of the sample is less than $38000.
Mathematics
1 answer:
Murrr4er [49]3 years ago
8 0
The probability is 0.9671.

The z-score for this is given by

z = (x - μ)/(σ/√n)
z = (38000-37500)/(1561/(√33)) = 1.84.

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of, less than, this is 0.9671.
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A random sample of n = 45 observations from a quantitative population produced a mean x = 2.5 and a standard deviation s = 0.26.
oee [108]

Answer:

P-value (t=2.58) = 0.0066.

Note: as we are using the sample standard deviation, a t-statistic is appropiate instead os a z-statistic.

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean μ exceeds 2.4.

Then, the null and alternative hypothesis are:

H_0: \mu=2.4\\\\H_a:\mu> 2.4

The significance level is 0.05.

The sample has a size n=45.

The sample mean is M=2.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.26.

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

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.26}{\sqrt{45}}=0.0388

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.5-2.4}{0.0388}=\dfrac{0.1}{0.0388}=2.58

The degrees of freedom for this sample size are:

df=n-1=45-1=44

This test is a right-tailed test, with 44 degrees of freedom and t=2.58, so the P-value for this test is calculated as (using a t-table):

P-value=P(t>2.5801)=0.0066

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

7 0
3 years ago
Which relation is a function?
diamong [38]

Answer:

A.

Step-by-step explanation:

If you use the vertical line test only one point hits the graph.

6 0
2 years ago
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The width of a rectangle is 7 less than the length. If the perimeter of the rectangle is 43.6 inches, what is the area of the re
Lera25 [3.4K]

Call the length a, the width b

Perimeter = (a+b) x 2

And since we have (a+b) x 2 = 43.6, a + b = 43.6 : 2 = 21.8

a + b = 21.8
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-> a + b + (a - b) = 28.8
2a = 28.8
a = 14.4
b = 7.4

So, the area of the rectangle is 14.4 x 7.4 = 106.56

8 0
2 years ago
Which set represents the same relation as the graph below?
Svetllana [295]

Answer:

start with root and minus with 3 and 8 and answer show

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2 years ago
12x-9y=36<br> X-intercept is<br> Y- intercept is
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Answer:

x-int is 3

y-int is -4

Step-by-step explanation:

when x is zero, -9y = 36

y = -4

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7 0
2 years ago
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