Mathematics, 05.05.2020 17:31 mt137896

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

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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 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.

7274717276

7077757272

7772757073

7475737474

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)

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 :

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

Answer from: Quest

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

Answer from: Quest

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