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Aleks [24]
3 years ago
9

A random sample of 45 professional football players indicated the mean height to be 6.18 feet with a sample standard deviation o

f 0.37 feet. A random sample of 40 professional basketball players indicated the mean height to be 6.45 feet with a standard deviation of 0.31 feet. Find a 95% confidence interval for the difference in mean heights of professional football and basketball players.
Mathematics
1 answer:
ch4aika [34]3 years ago
7 0

Answer:

Step-by-step explanation:

Hello!

The variables of interest are

X₁: height of a professional football player

n₁= 45

X[bar]₁= 6.18 feet

S₁= 0.37 feet

X₂: height of a professional basketball player

n₂= 40

X[bat]₂= 6.45 feet

S₂= 0.31 feet

You need to construct a 95%CI to estimate the difference between the mean heights of professional football players and basketball players.

To study the difference between the population means of two variables, you need these to have at least an approximately normal distribution. There is no information about the distributions of the variables so I'll assume that both study variables have a normal distribution and both population variances are equal.

The statistic you have to use to construct the interval is a t-test for independent samples with pooled sample variance:

(X[bar]₁-X[bar]₂)±t_{n_1+n_2-2;1-\alpha /2}*(Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} })

t_{n_1+n_2-2;1-\alpha /2}= t_{45+40-2;1-0.025}= t_{83;0.975}= 1.989

Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} }= \sqrt{\frac{44*0.37^2+39*0.31^2}{45+40-2} }=0.34

(6.18-6.45)±1.989*(0.34*\sqrt{\frac{1}{45} +\frac{1}{40} })

[-0.42;-0.12]

With a 95% confidence level, you'd expect that the interval [-0.42;-0.12]feet with contain the difference between the average height of professional football and basketball players.

I hope you have a SUPER day!

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Asked on December 20, 2019 by

Ziya Vïvəķ

A cylindrical container with diameter of base 56cm contains sufficient water to submerge a rectangular solid of iron with dimensions (32×22cm×14cm). Find the rise in the level of water when the solid is completely submerged.

MEDIUM

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ANSWER

Given,

Diameter of the base of the cylindrical container d=56 cm

Hence, radius of the base of the cylindrical container r=

2

56

=28 cm

Dimensions of rectangular solid is (32 cm×22 cm×14 cm)

We know that when a body is completely submerged in a container containing water,

the rise in the volume of water in the container is equal to the volume of the body.

Let, the water rises to a height h.

Hence,

Volume of water rises in cylindrical container =Volume of the rectangular solid

πr

2

h=32×22×14 cm

3

7

22

×(28)

2

×h=9856 cm

h=

22×784

9856×7

cm

h=4 cm

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