Question

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

1.6 | 2.4 | 1.2 | 6.6 | 2.3 | 0.0 | 1.8 | 2.5 | 6.5 | 1.8 |

2.7 | 2.0 | 1.9 | 1.3 | 2.7 | 1.7 | 1.3 | 2.1 | 2.8 | 1.4 |

3.8 | 2.1 | 3.4 | 1.3 | 1.5 | 2.9 | 2.6 | 0.0 | 4.1 | 2.9 |

1.9 | 2.4 | 0.0 | 1.8 | 3.1 | 3.8 | 3.2 | 1.6 | 4.2 | 0.0 |

1.2 | 1.8 | 2.4 |

(a) Use a calculator with mean and standard deviation keys to
find *x* and *s*. (Round your answers to two decimal
places.)

x = |
% |

s = |
% |

(b) Compute a 90% confidence interval for the population mean
*μ* of home run percentages for all professional baseball
players. *Hint:* If you use the Student's *t*
distribution table, be sure to use the closest *d.f.* that
is *smaller*. (Round your answers to two decimal
places.)

lower limit | % |

upper limit | % |

(c) Compute a 99% confidence interval for the population mean
*μ* of home run percentages for all professional baseball
players. (Round your answers to two decimal places.)

lower limit | % |

upper limit | % |

(d) The home run percentages for three professional players are
below.

Player A, 2.5 | Player B, 2.0 | Player C, 3.8 |

Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

We can say Player A falls close to the average, Player B is above average, and Player C is below average.We can say Player A falls close to the average, Player B is below average, and Player C is above average. We can say Player A and Player B fall close to the average, while Player C is above average.We can say Player A and Player B fall close to the average, while Player C is below average.

(e) In previous problems, we assumed the *x* distribution
was normal or approximately normal. Do we need to make such an
assumption in this problem? Why or why not? *Hint:* Use the
central limit theorem.

Yes. According to the central limit theorem, when *n* ≥
30, the *x* distribution is approximately normal.Yes.
According to the central limit theorem, when *n* ≤ 30, the
*x* distribution is approximately
normal. No. According to the central
limit theorem, when *n* ≥ 30, the *x* distribution is
approximately normal.No. According to the central limit theorem,
when *n* ≤ 30, the *x* distribution is approximately
normal.

Answer #1

a)from excel: x =average(array values )=2.29

s =stdev(array values )=1.40

b)

std error ='sx=s/√n=1.4010872221986/√43= | 0.2137 |

for 90% CI; and 42 df, value of t= | 1.682 |
from excel: t.inv(0.95,42) |
||

margin of error E=t*std error = | 0.36 | |||

lower bound=sample mean-E = |
1.93 |
|||

Upper bound=sample mean+E = |
2.65 |

c)

for 99% CI; and 42 df, value of t= | 2.698 |
from excel: t.inv(0.995,42) |
||

margin of error E=t*std error = | 0.58 | |||

lower bound=sample mean-E = |
1.72 |
|||

Upper bound=sample mean+E = |
2.87 |

d)

We can say Player A and Player B fall close to the average, while Player C is above average.

e)

No. According to the central limit theorem, when *n* ≥
30, the *x* distribution is approximately normal

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Compute a 90% confidence interval...

In baseball, is there a linear correlation between batting
average and home run percentage? Let x represent the
batting average of a professional baseball player, and let
y represent the player's home run percentage (number of
home runs per 100 times at bat). A random sample of n = 7
professional baseball players gave the following information.
x
0.235
0.249
0.286
0.263
0.268
0.339
0.299
y
1.3
3.2
5.5
3.8
3.5
7.3
5.0
(a) Make a scatter diagram of the...

In baseball, is there a linear correlation between batting
average and home run percentage? Let x represent the
batting average of a professional baseball player, and let
y represent the player's home run percentage (number of
home runs per 100 times at bat). A random sample of n = 7
professional baseball players gave the following information.
x
0.247
0.249
0.286
0.263
0.268
0.339
0.299
y
1.0
3.5
5.5
3.8
3.5
7.3
5.0
(b) Use a calculator to verify that...

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