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Svet_ta [14]
2 years ago
8

A publisher reports that 45% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is

actually different from the reported percentage. A random sample of 370 found that 40% of the readers owned a laptop. determine the p-value of the test statistic
Mathematics
1 answer:
nexus9112 [7]2 years ago
8 0

Answer:

z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933  

p_v =2*P(z  

Step-by-step explanation:

Information given

n=370 represent the sample selected

\hat p=0.4 estimated proportion of  readers owned a laptop

p_o=0.45 is the value that we want to test

z would represent the statistic

p_v represent the p value

Creating the hypothesis

We need to conduct a hypothesis in order to test if the true proportion of readers owned a laptop is different from 0.45, the system of hypothesis are:  

Null hypothesis:p=0.45  

Alternative hypothesis:p \neq 0.45  

The statistic is:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933  

Calculating the p value  

We have a bilateral test so then the p value would be:

p_v =2*P(z  

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Answer:

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3 years ago
(x^(2)-11x+30)/(x^(2)-25)*(x^(2)+6x+5)/(x-5x-6) simplify the rational expression
DanielleElmas [232]
Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))

The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))

The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))

x - 5 x = -4 x:
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6))

Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))

x^2 - 25 = x^2 - 5^2:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3))

Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3))

((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
((x - 6) (x + 1))/(-2 (2 x + 3))

Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:

Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
4 0
3 years ago
PLS HELP
Anika [276]

The chairs in the auditorium illustrates an arithmetic sequence

  • The recursive rule is:  an = an-1 + 8; a1 = 26
  • The explicit rule is:  an = 18 + 8n
  • There are 74 seats in the 7th row
  • 840 chairs can fit the auditorium

<h3>The recursive rule</h3>

From the question, we have the following sequence:

Seats: 18, 26, 34

Rewrite as:

26 = 18 + 8

34 = 26 + 8

The above means that:

The number of seats on a row is 8 added to the the number of seats on the previous row.

Hence, the recursive rule is:

an = an-1 + 8; a1 = 26

<h3>The explicit rule</h3>

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

an = 26 + (n - 1) * 8

Expand

an = 26 - 8 + 8n

Evaluate the difference

an = 18 + 8n

Hence, the explicit rule is:

an = 18 + 8n

<h3>The number of seats in the row 7</h3>

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

<h3>The sigma notation</h3>

We have the maximum number of rows to be 12.

So, the sigma notation would be:

\sum\limits^{12}_{n=1} {18 + 8n}

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

Read more about arithmetic sequence at:

brainly.com/question/6561461

7 0
2 years ago
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