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1 year ago

3.4.4 Journal: Exponential vs. Quadratic

Mathematics

1 answer:

zysi [14]1 year ago

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Answer:

what's the question your asking for?

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Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard dev

dangina [55]

Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches. a baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.5 inches. the heights (in inches) of 20 randomly selected players are shown in the table.

72 74 71 72 76

70 77 75 72 72

77 72 75 70 73

74 75 73 74 74

What are the correct hypotheses for this test?

The null hypothesis is H₀?: ____ 2.5

The alternative hypothesis is H₁?: ____ 2.5

Calculate the value of the test statistic.

x² = _____ (Round to three decimal places)

Answer:

Null hypothesis, H₀: σ = 2.5

Alternative hypothesis, Hₐ: μ<2.5

Test statistic = 12.920

Step-by-step explanation:

Given Data shows that:

men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches

We consider a random sample of 20 selected baseball players.

Therefore;

The Null and Alternative hypothesis are as follows:

The Null hypothesis is the standard deviation of the heights of major league baseball players is not less than 2.5 inches.

Null hypothesis, H₀: σ = 2.5

On the other hand: The Alternative hypothesis is the standard deviation of the heights of major league baseball players is less than 2.5 inches.

Alternative hypothesis, Hₐ: μ<2.5

The Mean Calculation is:

$\bar{x} = \frac{1}{2} \sum x_i$

$= \frac{1}{20} (72+74+...+74) \\ \\ = \frac{1468}{20} \\ \\ =73.4$

The sample standard deviation is:

$s = \sqrt{\frac{1}{n-1} \sum (x_1 - \bar{x})^2 }$

$= \sqrt{\frac{1}{20-1} \sum (72-73.4)^2 + ...+(74-73.4)^2 } \\ \\ = \sqrt{4.25} \\ \\ = 2.06$

The test statistics is now determined as :

$x^2 = \frac{(n-1)s^2}{\sigma^2} \\ \\ = \frac{(20-1)(2.06)^2}{(2.5)^2} \\ \\ = \frac{19*4.25}{6.25} \\ \\ = \frac{80.75}{6.25} \\ \\ = 12.920$

4 0

2 years ago

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in

ASHA 777 [7]

Answer:

a) There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c) The expected number of Chrome users is 4.074.

d) The variance for the number of Chrome users is 3.2441.

The standard deviation for the number of Chrome users is 1.8011.

Step-by-step explanation:

For each Internet browser user, there are only two possible outcomes. Either they use Chrome, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

Google Chrome has a 20.37% share of the browser market. This means that $p = 0.2037$

20 Internet users are sampled, so $n = 20$ .

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is P(X = 8).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243$

There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

Either there are less than 3 Chrome users, or there are three or more. The sum of the probabilities of these events is decimal 1. So:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105$

$P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538$

$P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.1950$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1950 = 0.8050$

There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c.For the sample of 20 Internet browser users, compute the expected number of Chrome users

We have that, for a binomial experiment:

$E(X) = np$

$E(X) = 20*0.2037 = 4.074$

The expected number of Chrome users is 4.074.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

We have that, for a binomial experiment, the variance is

$Var(X) = np(1-p)$

$Var(X) = 20*0.2037*(0.7963) = 3.2441$

The variance for the number of Chrome users is 3.2441.

The standard deviation is the square root of the variance. So

$\sqrt{Var(X)} = \sqrt{3.2441} = 1.8011$

The standard deviation for the number of Chrome users is 1.8011.

6 0

2 years ago

Which graph represents the function f(x) = -|x+3|?

Fofino [41]

The last one is correct

5 0

2 years ago

Read 2 more answers

The range for the Kentucky temperature is ____

natka813 [3]

Answer:

1) 6.1

2)5.1

3)2.8

4)2.4

5)I don't know what the last one is asking for, are there answer choices

Step-by-step explanation:

1)Max-min=58.3-52.2=6.1

2)Max-min=55-48.9=5.1

3)Upper quartile- lower quartile= 57.3-54.5=2.8

4)Upper quartile- lower quartile= 53.3-50.9=2.4

5) I don't know what this one is asking

6 0

1 year ago

Read 2 more answers

Alexa borrowed some money from her friend in order to help buy a new video game system. Alexa agreed to pay back her friend $10

Ulleksa [173]

Answer:

$L(t) = 170 - 10t$

Step-by-step explanation:

The amount that Alexa owes after t weeks is given by a linear equation in the following format:

$L(t) = L(0) - bt$

In which L(0) is the initial amount borrowed and b is how much is paid per week.

Alexa agreed to pay back her friend $10 per week and originally borrowed $170.

This means that, respectivelly, $b = 10, L(0) = 170$ . So

$L(t) = L(0) - bt$

$L(t) = 170 - 10t$

7 0

1 year ago